ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration

EXERCISE 16.1

Question 1.
Find the area of a triangle whose base is 6 cm and corresponding height is 4 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q1.1

Question 2.
Find the area of a triangle whose sides are
(i) 3 cm, 4 cm and 5 cm
(ii) 29 cm, 20 cm and 21 cm
(iii) 12 cm, 9.6 cm and 7.2 cm
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q2.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q2.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q2.3

Question 3.
Find the area of a triangle whose sides are 34 cm, 20 cm and 42 cm. Hence, find the length of the altitude corresponding to the shortest side.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q3.1

Question 4.
The sides of a triangular field are 975m, 1050 m and 1125 m. If this field is sold at the rate of Rs. 1000 per hectare, find its selling price. [1 hectare = 10000 m²].
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q4.2

Question 5.
The base of a right angled triangle is 12 cm and its hypotenuse is 13 cm long. Find its area and the perimeter.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q5.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q5.2

Question 6.
Find the area of an equilateral triangle whose side is 8 m. Given your answer correct to two decimal places.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q6.2

Question 7.
If the area of an equilateral triangle is 81√3 cm² find its. perimeter.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q7.1

Question 8.
If the perimeter of an equilateral triangle is 36 cm, calculate its area and height.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q8.2

Question 9.
(i) If the length of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 48 cm, find its area.
(ii) The sides of a triangular plot are in the ratio 3: 5:7 and its perimeter is 300 m. Find its area.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q9.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q9.2

Question 10.
ABC is a triangle in which AB = AC = 4 cm and ∠ A = 90°. Calculate the area of ∆ABC. Also find the length of perpendicular from A to BC.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q10.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q10.2

Question 11.
Find the area of an isosceles triangle whose equal sides are 12 cm each and the perimeter is 30 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q11.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q11.2

Question 12.
Find the area of an isosceles triangle whose base is 6 cm and perimeter is 16 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q12.1

Question 13.
The sides of a right angled triangle containing the right angle are 5x cm and (3x – 1) cm. Calculate the length of the hypotenuse of the triangle if its area is 60 cm².
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q13.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q13.2

Question 14.
In ∆ ABC, ∠B = 90°, AB = (2A + 1) cm and BC = (A + 1). cm. If the area of the ∆ ABC is 60 cm², find its perimeter.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q14.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q14.2

Question 15.
If the perimeter of a right angled triangle is 60 cm and its hypotenuse is 25 cm, find its area.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q15.1

Question P.Q.
In ∆ ABC, ∠B = 90° and D is mid-point of AC. If AB = 20 cm and BD = 14.5 cm, find the area and the perimeter of ∆ ABC.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Qp1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Qp1.2

Question 16.
The perimeter of an isosceles triangle is 40 cm. The base is two third of the sum of equal sides. Find the length of each side.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q16.1

Question 17.
If the area of an isosceles triangle is 60 cm2 and the length of each of its equal sides is 13 cm, find its base.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q17.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q17.2

Question 18.
The base of a triangular field is 3 times its height If the cost of cultivating the field at the rate of ₹25 per 100m2 is ₹60000, find its base and height.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q18.1

Question 19.
A triangular park ABC? has sides 120 m, 80 m and 50 m (as shown in the given figure). A gardner Dhania has to put a fence around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of ₹20 per metre leaving a space 3 m wide for a gate on one side.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q19.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q19.2

Question 20.
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (shown in the given figure), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q20.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q20.2

Question 21.
(a) In the figure (1) given below, ABC is an equilateral triangle with each side of length 10 cm. In ∆ BCD, ∠D = 90° and CD = 6 cm.
Find the area of the shaded region. Give your answer correct to one decimal place.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q21.1
(b) In the figure given, ABC is an isosceles right angled triangle and DEFG is a rectangle. If AD = AE = 3 cm and DB = EC = 4 cm, find the area of the shaded region.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q21.2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q21.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Q21.4

EXERCISE 16.2

Question 1.
(i) Find the area of quadrilateral whose one diagonal is 20 cm long and the perpendiculars to this diagonal from other vertices are of length 9 cm and 15 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q1.2

Question 2.
Find the area of the quadrilateral field ABCD whose sides AB = 40 m, BC = 28 m, CD = 15 m, AD = 9 m and ∠A = 90°
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q2.1

Question 3.
Find the area of the quadrilateral ABCD in which ∠BCA= 90°, AB = 13 cm and ACD is an equilateral triangle of side 12 cm.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q3.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q3.2

Question 4.
Find the area of quadrilateral ABCD in which ∠B = 90°, AB = 6 cm, BC = 8 cm 13 and CD = AD = 13 cm.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q4.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q4.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q4.3

Question 5.
The perimeter of a rectangular cardboard is 96 cm ; If its breadth is 18 cm, find the length and the area of the cardboard.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q5.1

Question 6.
The length of a rectangular hall is 5 m more than its breadth, If the area of the hall is 594 m2, find its perimeter.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q6.1
Solution:
Let ABCD be rectangular field.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q6.2

Question 7.
(a) The diagram (i) given below shows two paths drawn inside a rectangular field 50 m long and 35 m wide. The width of each path is 5 metres. Find the area of the shaded portion.
(b) In the diagram (ii) given below, calculate the area of the shaded portion. All measurements are in centimetres.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q7.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q7.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q7.3

Question 8.
A rectangular plot 20 m long and 14 m wide is to be covered with grass leaving 2 m all around. Find the area to be laid with grass.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q8.2

Question 9.
The shaded region of the given diagram represents the lawn in front of a house. On three sides of the lawn there are flower beds of width 2 m.
(i) Find the length and the breadth of the lawn.
(ii) Hence, or otherwise, find the area of the flower – beds.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q9.1
Solution:
BCDE is the lawn
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q9.2

Question 10.
A foot path of uniform width runs all around the inside of a rectangular field 50 m long and 38m wide. If the area of the path is 492 m². Find its width.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q10.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q10.2

Question 11.
The cost of enclosing a rectangular garden with a fence all around at the rate of Rs. 15 per metre is Rs. 5400. If the length of the garden is 100 m And the area of the garden.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q11.1

Question 12.
A rectangular floor which measures 15 m x 8 m is to be laid with tiles measuring 50 cm x 25 cm find the number of tiles required further, if a carpet is laid on the floor so that a space of 1 m exists between its edges and the edges of the floor, what fraction of the floor is uncovered?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q12.2

Question 13.
The width of a rectangular room is \(\frac { 3 }{ 5 }\) of its length x metres. If its perimeter isy metres, write an equation connecting.vandy. Find the floor area of the room if its perimeter is 32 m.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q13.1

Question 14.
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q14.1

Question 15.
A rectangular room is 6 m long, 4.8 m wide and 3.5 m high. Find the inner surface area of the four walls.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q15.1

Question 16.
A rectangular plot of land measures 41 metres in length and 22.5 metres in width. A boundary wall 2 metres high is built all around the plot at a distance of 1.5 m from the plot. Find the inner surface area of the boundary wall.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q16.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q16.2

Question 17.
(a) Find the perimeter and area of the figure
(i) given below in which all corners are right angled.
(b) Find the perimeter and area of the figure
(ii) given below in which all corners are right angles.
(c) Find the area and perimeter of the figure
(iii) given below in which all corners are right angles and all measurement in centimetres.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q17.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q17.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q17.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q17.4

Question 18.
The length and the breadth of a rectangle are 12 cm and 9 cm respectively. Find the height of a triangle whose base is 9 cm and whose area is one third that of rectangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q18.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q18.2

Question 19.
The area of a square plot is 484 mV Find the length of its one side and the length of its one diagonal.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q19.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q19.2

Question 20.
A square has the perimeter 56 m. Find its area and the length of one diagonal correct upto two decimal places.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q20.1

Question 21.
A wire when bent in the form of an equilateral triangle encloses an area of 36√3 cm2. Find the area enclosed by the same wire when bent to form:
(i) a square, and
(ii) a rectangle whose length is 2 cm more than its width.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q21.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q21.2

Question 22.
Two adjacent sides of a parallelogram are: 15 cm and 10 cm. If the distance between the longer sides is 8 cm, find the area of the parallelogram. Also find the distance between shorter sides.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q22.2

Question 23.
ABCD is a parallelogram with sides AB = 12 cm, BC = 10 cm and diagonal AC = 16 cm. Find the area of the parallelogram. Also find the distance between its shorter sides.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q23.1

Question 24.
Diagonals AC and BD of a parallelogram ABCD intersect at O. Given that AB = 12 cm and perpendicular distance between AB and DC is 6 cm. Calculate the area of the triangle AOD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q24.1

Question 25.
ABCD is a parallelogram with side AB = 10 cm. Its diagonals AC and BD are of length 12 cm and 16 cm respectively. Find the area of the parallelogram ABCD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q25.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q25.2

Question 26.
The area of a parallelogram is p cm2 and its height is q cm. A second parallelogram has equal area but its base is ‘r’ cm more than that of the first. Obtain an expression in terms of p, q and r for the height h of the second parallelogram.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q26.1

Question 27.
What is the area of a rhombus whose diagonals are 12 cm and 16 cm ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q27.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q27.2

Question 28.
The area of a rhombus is 98 cm². If one of its diagonal is 14 cm, what is the length of the other diagonal?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q28.1

Question 29.
The perimeter of a rhombus is 45 cm. If its height is 8 cm, calculate its area.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q29.1

Question 30.
PQRS is a rhombus. If it is given that PQ = 3 cm and the height of the rhombus is 2.5 cm, calculate its area.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q30.1

Question 31.
If the diagonals of a rhombus are 8 cm and 6 cm, find its perimeter.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q31.1

Question 32.
If the sides of a rhombus are 5 cm each and one diagonal is 8 cm, calculate
(i) the length of the other diagonal, and
(ii) the area of the rhombus.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q32.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q32.2

Question 33.
(a) The diagram (t) given below is a trapezium. Find the length of BC and the area of the trapezium Assume AB = 5 cm, AD = 4 cm, CD = 8 cm
(b) The diagram (ii) given below is a trapezium Find (i) AB (ii) area of trapezium ABCD.
(c) The cross-section of a canal is shown in figure (iii) given below. If the canal is 8 m wide at the top and 6 m wide at the bottom and the area of the cross-section is 16.8 m², calculate its depth
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q33.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q33.2

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q33.4

Question 34.
The distance between parallel sides of a trapezium is 12 cm and the distance between mid-points of other sides is 18 cm. Find the area of the trapezium.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q34.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q34.2

Question 35.
The area of a trapezium is 540 cm². If the ratio of parallel sides is 7 : 5 and the distance between them is 18 cm, find the length of parallel sides.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q35.1

Question 36.
The parallel sides of an isosceles trapezium are in the ratio 2 : 3. If its height is 4 cm and area is 60 cm2, find the perimeter.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q36.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q36.2

Question 37.
The area of a parallelogram is 98 cm². If one altitude is half the corresponding base, determine the base and the altitude of the parallelogram.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q37.1

Question 38.
The length of a rectangular garden is 12m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q38.1

Question 39.
If the perimeter of a rectangular plot is 68 m and length of its diagonal is 26 m, find its area.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q39.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q39.2

Question 40.
A rectangle has twice the area of a square. The length of the rectangle is 12 cm greater and the width is 8 cm greater than 2 side of a square. Find the perimeter of the square.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q40.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q40.2

Question 41.
The perimeter of a square is 48 cm. The area of a rectangle is 4 cm2 less than the area of the square. If the length of the rectangle is 4 cm greater than its breadth, find the perimeter of the rectangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q41.1

Question 42.
In the adjoining figure, ABCD is a rectangle with sides AB = 10 cm and BC = 8 cm. HAD and BFC are equilateral triangles; AEB and DCG are right angled isosceles triangles. Find the area of the shaded region and the perimeter of the figure.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q42.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q42.2

Question 43.
(a) Find the area enclosed by the figure (i) given below, where ABC is an equilateral triangle and DGFG is an isosceles trapezium.
All measurements are in centmetces.
(b) Find the area enclosed by the figure (ii) given below. AH measurements are in centimetres.
(c) In the figure (iii) given below, from a 24. cm x 24 cm piece of cardboard, a block in the shape of letter M is cut off. Find the area of the cardboard left over, all measurements are in centimetres.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q43.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q43.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q43.3

Question 44.
(a) The figure (i) given below shows the cross-section of the concrete structure with the measurements as given. Calculate the area of cross-section.
(b) The figure (ii) given below shows a field with the measurements given in metres. Find the area of the field.
(c) Calculate the area of the pentagon ABCDE shown in fig. (iii) below, given that AX = BX = 6 cm, EY = CY = 4 cm, DE = DC = 5cm,DX = 9cmand DX is perpendicular to EC and AB.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q44.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q44.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q44.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q44.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q44.5
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q44.6
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q44.7

Question 45.
If the length and the breadth of a room are increased by 1 metre the area is increased by 21 square metres. If the length is increased by 1 metre and breadth is decreased by 1 metre the, area is decreased by 5 square metres. Find the perimeter of the room.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q45.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q45.2

Question 46.
A triangle and a parallelogram have the same base and same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q46.1

Question 47.
A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that its perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q47.1

Question 48.
The perimeter of a rectangular plot is 180 m and its area is 1800 m². Take the length of plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the value of the length, breadth and the area to,write an equation in x. Solve the equation to calculate the length and breadth of the plot.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q48.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q48.2

EXERCISE 16.3

Question 1.
Find the length of the diameter of a circle whose circumference is 44 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q1.1

Question 2.
Find the radius and area of a circle if its circumference is 18π cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q2.1

Question 3.
Find the perimeter of a semicircular plate of radius 3.85 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q3.1

Question 4.
Find the radius and circumference of a circle whose area is 144π cm2.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q4.1

Question 5.
A sheet is 11 cm long and 2 cm wide. Circular pieces 0.5 cm in diameter are cut from it to prepare discs. Calculate the number of discs that can be prepared.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q5.1

Question 6.
If the area of a semicircular region is 77cm2, find its perimeter.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q6.2

Question 7.
(a) In the figure (i) given below, AC and BD are two perpendicular diameters of a circle ABCD. Given that the ara of the shaded portion is 308 cm2, calculate
(i) the length of AC and
(ii) the circumference of the circle.
(b) In the figure (ii) given below, AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take π = 3.14)
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q7.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q7.2

Question 8.
A bucket is raised from a well by means of a rope which is wound round a wheel of diameter 77 cm. Given that the bucket ascends in 1 minute 28 seconds with a uniform speed of 1.1 m/sec, calculate the number of complete revolutions the wheel makes in raising the bucket.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q8.1

Question 9.
The wheel of a cart is making 5 revolutions per second. If the diameter of the wheel is 84 cm, find its speed in km/hr. Give your answer correct to the nearest km.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q9.1

Question 10.
The circumference of a circle is 123.2 cm. Calculate :
(i) the radius of the circle in cm.
(ii) the area of the circle in cm2, correct to the nearest cm2.
(iii) the effect on the area of the circle if the radius is doubled.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q10.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q10.2

Question 11.
(a) In the figure (i) given below, the area enclosed between the concentric circles is 770 cm2. Given that the radius of the outer circle is 21 cm, calculate the radius of the inner circle.
(b) In the figure (ii) given below, the area enclosed between the circumferences of two concentric circles is 346.5 cm2. The circumference of the inner circle is 88 cm. Calculate the radius of the outer circle.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q11.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q11.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q11.3

Question 12.
A road 3.5 m wide surrounds a circular plot whose circumference is 44 m. Find the cost of paving the road at ₹50 per m2.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q12.1

Question 13.
The sum of diameters of two circles is 14 cm and the difference of their circumferences is 8 cm. Find the circumference of the two circles.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q13.1

Question 14.
Find the circumference of the circle whose area is equal to the sum of the areas of three circles with radius 2 cm, 3 cm and 6 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q14.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q14.2

Question 15.
A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q15.1

Question 16.
A copper wire when bent into an equilateral triangle has area 121√3 cm2. If the same wire is bent into the form of a circle, find the area enclosed by the wire.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q16.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q16.2

Question 17.
(a) Find the circumference of the circle whose area is 16 times the area of the circle with diameter 7 cm.
(b) In the given figure, find the area of the unshaded portion within the rectangle. (Take π = 3.14)
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q17.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q17.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 Q17.5

Question 18.
In the adjoining figure, A6CD is a square of side 21 cm. AC and BD are two diagonals of the square. Two semicircle are drawn with AD and BC as diameters. Find the area of the shaded region. Take π = \(\frac { 22 }{ 7 }\).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q18.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q18.2

Question 19.
(a) In the figure (i) given below, ABCD is a square of side 14 cm and APD and BPC are semicircles. Find the area and the perimeter of the shaded region.
(b) In the figure (ii) given below, ABCD is a square of side 14 cm. Find the area of the shaded region.
(c) In the figure (iii) given below, the diameter of the semicircle is equal to 14 cm. Calculate the area of the shaded region. Take π = \(\frac { 22 }{ 7 }\).
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q19.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q19.2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q19.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q19.4

Question 20.
(a) Find the area and the perimeter of the shaded region in figure (i) given below. The dimensions are in centimetres.
(b) In the figure (ii) given below, area of ∆ABC = 35 cm2. Find the area of the shaded region.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q20.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q20.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q20.3

Question 21.
(a) In the figure (i) given below, AOBC is a quadrant of a circle of radius 10 m. Calculate the area of the shaded portion. Take π = 3.14 and give your answer correct to two significant figures.
(b) In the figure, (ii) given below, OAB is a quadrant of a cirlce. The radius OA = 3.5 cm and OD = 2 cm. Calculate the area of the shaded portion.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q21.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q21.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q21.3

Question 22.
A student takes a rectangular piece of paper 30 cm long and 21 cm wide. Find the area of the biggest circle that can be cut out from the paper. Also find the area of the paper left after cutting out the circle. (Take π = \(\frac { 22 }{ 7 }\) )
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q22.2

Question 23.
A rectangle with one side 4 cm is inscribed in a circle of radius 2.5 cm. Find the area of the rectangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q23.1

Question 24.
(a) In the figure (i) given below, calculate the area of the shaded region correct to two decimal places. (Take π = 3. 142).
(b) In the figure (ii) given below, ABC is an isosceles right angled triangle with ∠ABC = 90°. A semicircle is drawn with AC as diameter. If AB = BC = 7 cm, find the area of the shaded region. Take π = \(\frac { 22 }{ 7 }\) .
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q24.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q24.2

Question 25.
A circular field has perimeter 660 m. A plot in the shape of a square having its vertices on the circumference is marked in the field. Calculate the area of the square field.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q25.1

Question 26.
In the adjoining figure, ABCD is a square. Find the ratio between
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q26.1
(i) the circumferences
(ii) the areas of the incircle and the circumcircle of the square.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q26.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q26.3

Question 27.
(a) The figure (i) given below shows a running track surrounding a grassed enclosure PQRSTU. The enclosure consists of a rectangle PQST with a semicircular region at each end.
PQ = 200 m ; PT = 70 m.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q27.1
(i) Calculate the area of the grassed enclosure in m2.
(ii) Given that the track is of constant width 7 m, calculate the outer perimeter ABCDEF of the track.
(b) In the figure (ii) given below, the inside perimeter of a practice running track with semi-circular ends and straight parallel sides is 312 m. The length of the straight portion of the track is 90 m. If the track has a uniform width of 2 m throughout, find its area.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q27.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q27.3

Question 28.
(a) In the figure (i) given below, two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.
(b) The quadrants shown in the figure (ii) given below are each of radius 7 cm. Calculate the area of the shaded portion.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q28.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q28.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q28.3

Question 29.
(a) In the figure (i) given below, two circular flower beds have been shown on the two sides of a square lawn ABCD of side 56 m. If the centre of each circular flower bed is the point of intersection O of the diagonals of the square lawn, find the sum of the areas of the lawn and the flower beds.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q29.1
(b) In the figure (ii) given below, a square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q29.2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q29.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q29.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q29.5

Question 30.
(a) In the figure (i) given below, ABCD is a rectangle, AB = 14 cm and BC = 7 cm. Taking DC, BC and AD as diameters, three semicircles are drawn as shown in the figure. Find the area of the shaded portion.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q30.1
(b) In the figure (ii) given below, O is the centre of a circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of the shaded region. (Use π = 3.14).
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q30.2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q30.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q30.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q30.5
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q30.6

Question 31.
(a) In the figure given below ABCD is a square of side 14 cm. A, B, C and D are centres of the equal circle which touch externally in pairs. Find the area of the shaded region.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q31.1
(b) In the figure (ii) given below, the boundary of the shaded region in the given diagram consists of three semi circular arcs, the smaller being equal. If the diameter of the larger one is 10 cm, calculate.
(i) the length of the boundary.
(ii) the area of the shaded region. (Take π to be 3.14)
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q31.2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q31.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q31.4

Question 32.
(a) In the figure (i) given below, the points A, B and C are centres of arcs of circles of radii 5 cm, 3 cni and 2 cm respectively. Find the perimeter and the area of the shaded region. (Take π = 3.14).
(b) In the figure (ii) given below, ABCD is a square of side 4 cm. At each corner of the square a quarter circle of radius 1 cm, and at the centre a circle of diameter 2 cm are drawn. Find the perimeter and the area of the shaded region. Take π = 3.14.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q32.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q32.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q32.3

Question 33.
(a) In the figure given below, ABCD is a rectangle. AB = 14 cm, BC = 7 cm. From the rectangle, a quarter circle BFEC and a semicircle DGE are removed. Calculate the area of the remaining piece of the rectangle. (Take π = 22/7)
(b) The figure (ii) given below shows a kite, in which BCD is in the shape of a quadrant of circle of radius 42 cm. ABCD is a square and ∆ CEF is an isosceles right angled triangle whose equal sides are 6 cm long. Find the area of the shaded region.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q33.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q33.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q33.3

Question 34.
(a) In the figure (i) given below, the boundary of the shaded region in the given diagram consists of four semi circular arcs, the smallest two being equal. If the diameter of the largest is 14 cm and of the smallest is 3.5 cm, calculate
(i) the length of the boundary.
(ii) the area of the shaded region.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q34.1
(b) In the figure (ii) given below, a piece of cardboard, in the shape of a trapezium ABCD, and AB || DC and ∠BCD = 90°, quarter circle BFEC is removed. Given AB = BC = 3.5 cm and DE = 2 cm. Calculate the area of the remaining piece of the cardboard.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q34.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q34.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q34.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q34.5

Question 35.
(a) In the figure (i) given below, ABC is a right angled triangle, ∠B = 90°, AB = 28 cm and BC = 21 cm. With AC as diameter a semi-circle is drawn and with BC as radius a quarter circle is drawn. Find the area of the shaded region correct to two decimal places.
(b) In the figure (ii) given below, ABC is an equilateral triangle of side 8 cm. A, B and C are the centres of circular arcs of equal radius. Find the area of the shaded region correct upto 2 decimal places.    (Take π = 3.142 and √3 = 1.732).
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q35.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q35.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q35.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q35.4

Question 36.
A circle is inscribed in a regular hexagon of side 2√3 cm. Find
(i) the circumference of the inscribed circle
(ii) the area of the inscribed circle
Solution:
ABCDEF is a regular hexagon of side 2√3 cm. and a circle is inscribed in it with centre O.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q36.1

Question 37.
In the figure (i) given below, a chord AB of a circle of radius 10 cm subtends a right angle at the centre O. Find the area of the sector OACB and of the major segment. Take π = 3.14.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q37.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.3 Q37.2

EXERCISE 16.4

Question 1.
Find the surface area and volume of a cube whose one edge is 7 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q1.1

Question 2.
Find the surface area and the volume of a rectangular solid measuring 5 m by 4 m by 3 m. Also find the length of a diagonal.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q2.1

Question 3.
The length and breadth of a rectangular solid are respectively 25 cm and 20 cm. If the volume is 7000 cm3, find its height.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q3.1

Question 4.
A class room is 10 m long, 6 m broad and 4 m high. How many students can it accommodate if one student needs 1.5 m2 of floor area ? How many cubic metres of air will each student have ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q4.2

Question 5.
(a) The volume of a cuboid is 1440 cm3. Its height is 10 cm and the cross-section is a square. Find the side of the square.
(b) The perimeter of one face of a cube is 20 cm. Find the surface area and the volume of the cube.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q4.2

Question 6.
Mary wants to decorate her Christmas tree. She wants to place the tree on a wooden box covered with coloured papers with pictures of Santa Claus. She must know the exact quantity of paper to buy for this purpose. If the box has length 80 cm, breadth 40 cm and height 20 cm respectively, then how many square sheets of paper of side 40 cm would she require ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q6.1

Question 7.
The volume of a cuboid is 3600 cm3 and its height is 12 cm. The cross-section is a rectangle whose length and breadth are in the ratio 4 :3. Find the perimeter of the cross-section.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q7.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q7.2

Question 8.
The volume of a cube is 729 cm3. Find its surface area and the length of a diagonal.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q8.1

Question 9.
The length of the longest rod which can be kept inside a rectangular box is 17 cm. If the inner length and breadth of the box are 12 cm and 8 cm respectively, find its inner height.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q9.1

Question 10.
A closed rectangular box has inner dimensions 90 cm by 80 cm by 70 cm. Calculate its capacity and the area of tin-foil needed to line its inner surface.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q10.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q10.2

Question 11.
The internal measurements of a box are 20 cm long, 16 cm wide and 24 cm high. How many 4 cm cubes could be put into the box ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q11.1

Question 12.
The internal measurements of a box are 10 cm long, 8 cm wide and 7 cm high. How many cubes of side 2 cm can be put into the box ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q12.1

Question 13.
A certain quantity of wood costs Rs. 250 per m3. A solid cubical block of such wood is bought for Rs. 182.25. Calculate the volume of the block and use the method of factors to find the length of one edge of the block.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q13.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q13.2

Question 14.
A cube of 11 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base of the vessel are 15 cm x 12 cm, find the rise in the water level in centimetres correct to 2 decimal places, assuming that no water over flows.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q14.1

Question 15.
A rectangular container, whose base is a square of side 6 cm, stands on a horizontal table and holds water upto 1 cm from the top. When a cube is placed in the water and is completely submerged, the water rises to the top and 2 cm3 of water over flows.. Calculate the volume of the cube.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q15.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q15.2

Question 16.
(a) Two cubes, each with 12 cm edge, are joined end to end. Find the surface area of the resulting cuboid,
(b) A solid cube of side 12 cm is cut into eight cubes of equal volume. What will be the side of the new cube ? Also, find the ratio between the surface area of the original cube and the sum of the surface areas of the new cubes.

Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q16.1

Question 17.
A cube of a metal of 6 cm edge is melted and cast into a cuboid whose base is 9 cm x g cm. Find the height of the cuboid.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q17.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q17.2

Question 18.
The area of a playground is 4800 m2. Find the cost of covering it with gravel 1 cm deep, if the gravel costs Rs. 260 per cubic metre.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q18.1

Question 19.
A field is 30 m long and 18 m broad. A pit 6 m long, 4m wide and 3 m deep is dug out from the middle of the field and the earth removed is evenly spread over the remaining area of the field. Find the rise in the level of the remaining part of the field in centimetres correct to two decimal places.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q19.1

Question 20.
A rectangular plot is 24 m long and 20 m wide. A cubical pit of edge 4 m is dug at each of the four corners of the field and the soil removed is evenly spread over the remaining part of the plot. By what height does the remaining plot get raised?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q20.1

Question 21.
The inner dimensions of a closed wooden box are 2 m, 1.2 m and .75 m. The thickness of the wood is 2.5 cm. Find the cost of wood required to make the box if 1 m3 of wood costs Rs. 5400.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q21.1

Question 22.
A cubical wooden box of internal edge 1 mis made of 5 cm thick wood. The box is open at the top. If the wood costs Rs. 9600 per cubic metre, find the cost of the wood required to make the box.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q22.1

Question 23.
A square brass plate of side x cm is 1mm thick and weighs 4725 g. If one. cc of brass weighs 8.4 gm, find the value of x.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q23.1

Question 24.
Three cubes whose edges are x cm, 8 cm and 10 cm respectively are melted and recast into a single cube of edge 12 cm. Find x.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q24.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q24.2

Question 25.
The area of cross-section of a pipe is 3.5 cm2 and water is flowing out of pipe at the rate of 40 cm/s. How much water is delivered by the pipe in one minute ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q25.1

Question 26.
(a) The figure (i) given below shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in cm and all angles in the figure are right angles.
(b) The figure (ii) given below shows the cross section of a concrete wall to be constructed. It is 2 m wide at the top, 3.5 m wide at the bottom and its
height is 6 m, and its length is 400 m. Calculate (i) The cross-sectional area, and (ii) volume of concrete in the wall.
(c) The figure (iii) given below show the cross section of a swimming pool 10 m broad, 2 m deep at one end and 3 m deep at the other end. Calculate the volume of water it will hold when full, given that its length is 40 m.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q26.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q26.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q26.3

Question 27.
A swimming pool is 50 metres long and 15 metres wide. Its shallow and deep ends arc 1\(\frac { 1 }{ 2 }\) metres and 14\(\frac { 1 }{ 2 }\) metres deep respectively. If the bottom of the pool slopes uniformly, find the amount of water required to fill the pool.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q27.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.4 Q27.2

Multiple Choice Questions

Choose the correct answer from the given four options (1 to 24):
Question 1.
Area of a triangle is 30 cm2. If its base is 10 cm, then its height is
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q1.1

Question 2.
If the perimeter of a square is 80 cm, then its area is
(a) 800 cm2
(b) 600 cm2
(c) 400 cm2
(d) 200 cm2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q2.1

Question 3.
Area of a parallelogram is 48 cm2. If its height is 6 cm then its base is
(a) 8 cm
(b) 4 cm
(c) 16 cm
(d) None of these
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q3.1

Question 4.
If d is the diameter of a circle, then its area is
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q4.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q4.2

Question 5.
If the area of a trapezium is 64 cm2 and the distance between parallel sides is 8 cm, then sum of its parallel sides is
(a) 8 cm
(b) 4 cm
(c) 32 cm
(d) 16 cm
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q5.1

Question 6.
Area of a rhombus whose diagonals are 8 cm and 6 cm is
(a) 48 cm2
(b) 24 cm2
(c) 12 cm2
(d) 96 cm2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q6.1

Question 7.
If the lengths of diagonals of a rhombus is doubled, then area of rhombus will be
(a) doubled
(b) tripled
(c) four times
(d) remains same
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q7.1

Question 8.
If the length of a diagonal of a quadrilateral is 10 cm and lengths of the perpendiculars on it from opposite vertices are 4 cm and 6 cm, then area of quadrilateral is
(a) 100 cm2
(b) 200 cm2
(c) 50 cm2
(d) None of these
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q8.2

Question 9.
Area of a rhombus is 90 cm2. If the length of one diagonal is 10 cm then the length of other diagonal is
(a) 18 cm
(b) 9 cm
(c) 36 cm
(d) 4.5 cm
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q9.1

Question 10.
In the given figure, OACB is a quadrant of a circle of radius 7 cm. The perimeter of the quadrant is
(a) 11 cm
(b) 18 cm
(c) 25 cm
(d) 36 cm
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q10.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q10.2

Question 11.
In the given figure, OABC is a square of side 7 cm. OAC is a quadrant of a circle with O as centre. The area of the shaded region is
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q11.1
(a) 10.5 cm2
(b) 38.5 cm
(c) 49 cm2
(d) 11.5 cm2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q11.2

Question 12.
The given figure shows a rectangle and a semicircle. The perimeter of the shaded region is
(a) 70 cm
(b) 56 cm
(c) 78 cm
(d) 46 cm
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q12.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q12.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q12.3

Question 13.
The area of the shaded region shown in Q. 12 (above is
(a) 140 cm2
(b) 77 cm2
(c) 294 cm2
(d) 217 cm2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q13.1

Question 14.
In the given figure, the boundary of the shaded region consists of semicircular arcs. The area of the shaded region is equal to
(a) 616 cm2
(b) 385 cm2
(c) 231 cm2
(d) 308 cm2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q14.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q14.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q14.3

Question 15.
The perimeter of the shaded region shown in Q. 14 (above) is
(a) 44 cm
(b) 88 cm
(c) 66 cm
(d) 132 cm
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q15.1

Question 16.
In the given figure, ABC is a right angled triangle at B. A semicircle is drawn on AB as diameter. If AB = 12 cm and BC = 5 cm, then the area of the shaded region is
(a) (60 + 18π) cm2
(b) (30 + 36π) cm2
(c) (30+18π) cm2
(d) (30 + 9π) cm2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q16.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q16.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q16.3

Question 17.
The perimeter of the shaded region shown in Q. 16 (above) is
(a) (30 + 6π) cm
(b) (30 + 12π) cm
(c) (18 + 12π) cm
(d) (18 + 6π) cm
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q17.1

Question 18.
If the volume of a cube is 729 m3, then its surface area is
(a) 486 cm2
(b) 324 cm2
(c) 162 cm2
(d) None of these
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q18.1

Question 19.
If the total surface area of a cube is 96 cm2, then the volume of the cube is
(a) 8 cm3
(b) 512 cm3
(c) 64 cm3
(d) 27 cm3
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q19.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q19.2

Question 20.
The length of the longest pole that can be put in a room of dimensions (10 m x 10 m x 5 m) is
(a) 15 m
(b) 16 m
(c) 10 m
(d) 12 m
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q20.1

Question 21.
The lateral surface area of a cube is 256 m2. The volume of the cube is
(a) 512 m3
(b) 64 m3
(c) 216 m3
(d) 256 m3
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q21.1

Question 22.
If the perimeter of one face of a cube is 40 cm, then the sum of lengths of its edge is
(a) 80 cm
(b) 120 cm
(c) 160 cm
(d) 240 cm
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q22.1

Question 23.
A cuboid container has the capacity to hold 50 small boxes. If all the dimensions of the container are doubled, then it can hold (small boxes of same size)
(a) 100 boxes
(b) 200 boxes
(c) 400 boxes
(d) 800 boxes
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q23.1

Question 24.
The number of planks of dimensions (4 m x 50 cm x 20 cm) that can be stored in a pit which is 16 m long, 12 m wide and 4 m deep is
(a) 1900
(b) 1920
(c) 1800
(d) 1840
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration mul Q24.1

Chapter Test

Question 1.
(a) Calculate the area of the shaded region.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration ch Q1.1
(b) If the sides of a square are lengthened by 3 cm, the area becomes 121 cm2. Find the perimeter of the original square.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration ch Q1.2

Question P.Q.
The given figure shows a kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and side 6cm each. How much paper is used in making the kite ? Ignore the wastage of the paper is making the kite.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Qp2.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration Qp2.2

Question 2.
(a) Find the area enclosed by the figure (i) given below. All measurements are in centimetres:
(b) Find the area of the quadrilateral ABCD shown in figure (ii) given below. All measurements are in centimetres.
(c) Calculate the area of the shaded region shown in figure (iii) given below. All measurements are in metres.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 2.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 2.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 2.3

Question 3.
Asifa cut an aeroplane from a coloured chart paper (as shown in the adjoining figure). Find the total area of the chart paper used, correct to 1 decimal place.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 3.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 3.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 3.3

Question 4.
If the area of a circle is 78.5 cm2, find its circumference. (Take π = 3.14)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 4.1

Question 5.
From a square cardboard, a circle of biggest area was cut out. If the area of the circle is 154 cm2, calculate the original area of the cardboard.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 5.2

Question 6.
(a) From a sheet of paper of dimensions = 2m x 1.5m, how many circles can you cut of radius 5cm. Also find the area of the paper wasted. Take π = 3.14.
(b) If the diameter of a semicircular protractor is 14cm, then find its perimeter.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 6.2

Question 7.
A road 3.5 m wide surrounds a circular park whose circumference is 88 m. Find the cost of paving the road at the rate of Rs. 60 per square metre.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 7.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 7.2

Question 8.
The adjoining sketch shows a running tract 3.5 m wide all around which consists of two straight paths and two semicircular rings. Find the area of the track.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 8.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 8.2

Question 9.
In the adjoining figure, O is the centre of a circular arc and AOB is a line segment.Find the perimeter and the area of the shaded region correct to one decimal place. (Take π = 3.142)
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 9.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 9.2

Question 10.
(a) In the figure (1) given below, the radius is 3.5 cm. Find the perimeter of the quarter of the circle.
(b) In the figure (ii) given below, there are five squares each of side 2 cm.
(i) Find the radius of the circle.
(ii) Find the area of the shaded region. (Take π= 3.14).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 10.1

Question 11.
(a) In the figure (i) given below, a piece of cardboard in the shape of a quadrant of a circle of radius 7 cm is bounded by perpendicular radii OX and OY. Points A and B lie on OX and OY respectively such that OA = 3 cm and OB = 4 cm. The triangular part OAB is removed. Calculate the area and the perimeter of the remaining piece.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.2 11.1
(b) In the figure (ii) given below, ABCD is a square. Points A, B, C and D are centres of quadrants of circles of the same radius. If the area of the shaded portion is 21\(\frac { 3 }{ 7 }\)
cm2, find the radius of the quadrants. Take π = \(\frac { 22 }{ 7 }\).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 11.2

Question 12.
In the adjoining figure, ABC is a right angled triangle right angled at B. Semicircle are drawn on AB, BC and CA as diameter. Show that the sum of areas of semi circles drawn on AB and BC as diameter is equal to the area of the semicircle drawn on CA as diameter.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 12.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 12.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 12.3

Question 13.
The length of minute hand of a clock is 14 cm. Find the area swept by the minute hand in 15 minutes.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 13.1

Question 14.
Find the radius of a circle if a 90° arc has a length of 3.5 n cm. Hence, find the area of sector formed by this arc.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 14.1

Question 15.
A cube whose each edge is 28 cm long has a circle of maximum radius on each of its face painted red. Find the total area of the unpainted surface of the cube.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 15.1

Question 16.
Can a pole 6.5 m long fit into the body of a truck with internal dimensions of 3.5m, 3 m and 4m?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 16.1

Question 17.
A car has a petrol tank 40 cm long, 28 cm wide and 25 cm deep. If the fuel consumption of the car averages 13.5 km per litre, how far can the car travel with a full tank of petrol ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 17.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 17.2

Question 18.
An aquarium took 96 minutes to completely fill with water. Water was filling the aquarium at a rate of 25 litres every 2 minutes. Given that the aquarium was 2 m long and 80 cm wide, compute the height of the aquarium.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 18.1

Question 19.
The lateral surface area of a cubiod is 224 cm2. Its height is 7 cm and the base is a square. Find :
(i) a side of the square, and
(ii) the volume of the cubiod.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 19.1

Question 20.
If the volume of a cube is V m3, its surface area is S m2 and the length of a diagonal is d metres, prove that 6√3 V = S d.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 20.1

Question 21.
The adjoining figure shows a victory stand, each face is rectangular. All measurement are in centimetres. Find its volume and surface area (the bottom of the stand is open).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 21.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 21.2

Question 22.
The external dimensions of an open rectangular wooden box are 98 cm by 84 cm by 77 cm. If the wood is 2 cm thick all around, find :
(i) the capacity of the box
(ii) the volume of the wood used in making the box, and
(iii) the weight of the box in kilograms correct to one decimal place, given that 1 cm3 of wood weighs 0.8 gm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 22.2

Question 23.
A cuboidal block of metal has dimensions 36 cm by 32 cm by 0.25 m. It is melted and recast into cubes with an edge of 4 cm.
(i) How many such cubes can be made ?
(ii) What is the cost of silver coating the surfaces of the cubes at the rate of Rs. 1.25 per square centimetre ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 23.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 23.2

Question 24.
Three cubes of silver with edges 3 cm, 4 cm and 5 cm are melted and recast into a single cube. Find the cost of coating the surface of the new cube with gold at the rate of Rs. 3.50 per square centimetre.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 24.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 16 Mensuration 24.2

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry

EXERCISE 19.1

Question 1.
Find the co-ordinates of points whose
(i) abscissa is 3 and ordinate -4.
(ii) abscissa is – \(\frac { 3 }{ 2 }\)and ordinate 5.
(iii) whose abscissa is -1\(\frac { 2 }{ 3 }\) and ordinate -2 \(\frac { 1 }{ 4 }\) .
(iv) whose ordinate is 5 and abscissa is -2
(v) whose abscissa is -2 and lies on x-axis.
(vi) whose ordinate is \(\frac { 3 }{ 2 }\) and lies on y-axis.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q1.1

Question 2.
In which quadrant or on which axis each of the following points lie?
(-3, 5), (4, -1) (2, 0), (2, 2), (-3, -6)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q2.1

Question 3.
Which of the following points lie on
(i) x-axis? (ii) y-axis?
A (0, 2), B (5, 6), C (23, 0), D (0, 23), E (0, -4), F (-6, 0), G (√3,0)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q3.1

Question 4.
Plot the following points on the same graph paper :
A (3, 4), B (-3, 1), C (1, -2), D (-2, -3), E (0, 5), F (5, 0), G (0, -3), H (-3, 0).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q4.1

Question 5.
Write the co-ordinates of the points A, B, C, D, E, F, G and H shown in the adjacent figure.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q5.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q5.2

Question 6.
In which quadrants are the points A, B, C and D of problem 3 located ?
Solution:
A Lies in the first quadrant, B lies on x-axis C lies in the third quadrant and D lies in the fourth quadrant.

Question 7.
Plot the following points on the same graph paper :
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q7.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q7.2

Question 8.
Plot the following points on the same graph paper.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q8.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q8.2

Question 9.
Plot the following points and check whether they are collinear or not:
(i) (1,3), (-1,-1) and (-2,-3)
(ii) (1,2), (2,-1) and (-1, 4)
(iii) (0,1), (2, -2) and (\(\frac { 2 }{ 3 }\) ,0)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q9.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q9.2

Question 10.
Plot the point P(-3, 4). Draw PM and PN perpendiculars to x-axis and y-axis respectively. State the co-ordinates of the points M and N.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q10.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q10.2

Question 11.
Plot the points A (1,2), B (-4,2), C (-4, -1) and D (1, -1). What kind of quadrilateral is ABCD ? Also find the area of the quadrilateral ABCD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q11.1

Question 12.
Plot the points (0,2), (3,0), (0, -2) and (-3,0) on a graph paper. Join these points (in order). Name the figure so obtained and find the area of the figure obtained.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q12.2

Question 13.
Three vertices of a square are A (2,3), B(-3, 3) and C (-3, -2). Plot these points on a graph paper and hence use it to find the co-ordinates of the fourth vertex. Also find the area of the square.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q13.1

Question 14.
Write the co-ordinates of the vertices of a rectangle which is 6 units long and 4 units wide if the rectangle is in the first quadrant, its longer side lies on the x-axis and one vertex is at the origin.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q14.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q14.2

Question 15.
Repeat problem 12 assuming that the rectangle is in the third quadrant with all other conditions remaining the same.
Solution:
A rectangle which is 6 unit long and 4 units wide and this rectangle is in the third quadrant.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q15.1

Question 16.
The adjoining figure shows an equilateral triangle OAB with each side = 2a units. Find the coordinates of the vertices.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q16.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q16.2

Question 17.
In the given figure, APQR is equilateral. If the coordinates of the points Q and R are (0, 2) and (0, -2) respectively, find the coordinates of the point P.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q17.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q17.2

EXERCISE 19.2

Question 1.
Draw the graphs of the following linear equations :
(i) 2x + + 3 = 0
(ii) x- 5y- 4 = 0
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q1.2

Question 2.
Draw the graph of 3y= 12 – 2x. Take 2cm = 1 unit on both axes.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q2.1

Question 3.
Draw the graph of 5x + 6y – 30 = 0 and use it to find the area of the triangle formed by the line and the co-ordinate axes.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q3.1

Question 4.
Draw the graph of 4x- 3y + 12 = 0 and use it to find the area of the triangle formd by the line and the co-ordinate axes. Take 2 cm = 1 unit on both axes.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q4.2

Question 5.
Draw the graph of the equation y = 3x – 4. Find graphically.
(i) the value of y when x = -1
(ii) the value of x when y = 5.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q5.2

Question 6.
The graph of a linear equation in x and y passes through (4, 0) and (0, 3). Find the value of k if the graph passes through (A, 1.5).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q6.1

Question 7.
Use the table given alongside to draw the graph of a straight line. Find, graphically the values of a and b.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q7.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.2 Q7.2

EXERCISE 19.3

Question 1.
Solve the following equations graphically: 3x – 2y = 4, 5x – 2y = 0
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q1.2

Question 2.
Solve the following pair of equations graphically. Plot at least 3 points for each straight line 2x – 7y = 6, 5x – 8y = – 4
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q2.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q2.2

Question 3.
Using the same axes of co-ordinates and the same unit, solve graphically.
x+y = 0, 3x – 2y = 10
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q3.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q3.2

Question 4.
Take 1 cm to represent 1 unit on each axis to draw the graphs of the equations 4x- 5y = -4 and 3x = 2y – 3 on the same graph sheet (same axes). Use your graph to find the solution of the above simultaneous equations.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q4.2

Question 5.
Solve the following simultaneous equations graphically, x + 3y = 8, 3x = 2 + 2y
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q5.2

Question 6.
Solve graphically the simultaneous equations 3y = 5 – x, 2x = y + 3 (Take 2cm = 1 unit on both axes).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q6.2

Question 7.
Use graph paper for this question.
Take 2 cm = 1 unit on both axes.
(i) Draw the graphs of x +y + 3 = 0 and 3x-2y + 4 = 0. Plot only three points per line.
(ii) Write down the co-ordinates of the point of intersection of the lines.
(iii) Measure and record the distance of the point of intersection of the lines from the origin in cm.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q7.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q7.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q17.5
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry Q17.4

Question 8.
Solve the following simultaneous equations graphically :
2x-3y + 2 = 4x+ 1 = 3x – y + 2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q8.1

Question 9.
Use graph paper for this question.
(i) Draw the graphs of 3x -y – 2 = 0 and 2x + y – 8 = 0. Take 1 cm = 1 unit on both axes and plot three points per line.
(ii) Write down the co-ordinates of the point of intersection and the area of the traingle formed by the lines and the x-axis.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q9.1

Question 10.
Solve the following system of linear equations graphically : 2x -y – 4 = 0, x + y + 1 = 0. Hence, find the area of the triangle formed by these lines and the y-axis.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q10.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q10.2

Question 11.
Solve graphically the following equations: x + 2y = 4, 3x – 2y = 4
Take 2 cm = 1 unit on each axis. Write down the area of the triangle formed by the lines and the x-axis.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q11.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q11.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q11.3

Question 12.
On graph paper, take 2 cm to represent one unit on both the axes, draw the lines : x + 3 = 0, y –  2 = 0, 2x + 3y = 12 .
Write down the co-ordinates of the vertices of the triangle formed by these lines.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q12.2

Question 13.
Find graphically the co-ordinates of the vertices of the triangle formed by the lines y = 0, y – x and 2x + 3y= 10. Hence find the area of the triangle formed by these lines.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q13.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q13.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.3 Q13.3

EXERCISE 19.4

Question 1.
Find the distance between the following pairs of points :
(i) (2, 3), (4, 1)
(ii) (0, 0), (36, 15)
(iii) (a, b), (-a, -b)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q1.2

Question 2.
A is a point on y-axis whose ordinate is 4 and B is a point on x-axis whose abscissa is -3. Find the length of the line segment AB.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q2.1

Question 3.
Find the value of a, if the distance between the points A (-3, -14) and B (a, -5) is 9 units.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q3.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q3.2

Question 4.
(i) Find points on the x-axis which are at a distance of 5 units from the point (5, -4).
(ii) Find points on the y-axis are at a distance of 10 units from the point (8, 8) ?
(iii) Find points (or points) which are at a distance of √10 from the point (4, 3) given that the ordinate of the point or points is twice the abscissa.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q4.2

Question 5.
Find the point on the x-axis which, is equidistant from the points (2, -5) and (-2, 9).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q5.2

Question 6.
Find the value of x such that PQ = QR where the coordinates of P, Q and R are (6, -1), (1, 3) and (x, 8) respectively.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q6.1

Question 7.
If Q (0, 1) is equidistant from P (5, -3) and R (x, 6) find the values of x.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q7.1

Question 8.
Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q8.2

Question 9.
The x-coordinate of a point P is twice its y-coordinate. If P is equidistant from the points Q (2, -5) and U (-3, 6), then find the coordinates of P.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q9.1

Question 10.
If the points A (4,3) and B (x, 5) are on a circle with centre C (2, 3), find the value of x.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q10.1

Question 11.
If a point A (0, 2) is equidistant from the points B (3, p) and C (p, 5), then find the value of p.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q11.1

Question 12.
Using distance formula, show that (3, 3) is the centre of the circle passing through the points (6, 2), (0, 4) and (4, 6).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q12.1

Question 13.
The centre of a circle is C (2α – 1, 3α + 1) and it passes through the point A (-3, -1). If a diameter of the circle is of length 20 units, find the value(s) of α.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q13.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q13.2

Question 14.
Using distance formula, show that the points A (3, 1), B (6, 4) and C (8, 6) are coliinear.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q14.1

Question 15.
Check whether the points (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q15.1

Question 16.
Name the type of triangle formed by the points A (-5, 6), B (-4, -2) and (7, 5).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q16.1

Question 17.
Show that the points (1, 1), (- 1, – 1) and (-√3,√3) form an equilateral triangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q17.1

Question 18.
Show that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q18.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q18.2

Question 19.
The points A (0, 3), B (- 2, a) and C (- 1, 4) are the vertices of a right angled triangle at A, find the value of a.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q19.1

Question 20.
Show that the points (0, – 1), (- 2, 3), (6, 7) and (8, 3), taken in order, are the vertices of a rectangle. Also find its area.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q20.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q20.2

Question 21.
If P (2, -1), Q (3, 4), R (-2, 3) and S (-3, -2) be four points in a plane, show that PQRS is a rhombus but not a square. Find the area of the rhombus.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q21.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q21.2

Question 22.
Prove that the points A (2, 3), B {-2, 2), C (-1, -2) aqd D (3, -1) are the vertices of a square ABCD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q22.2

Question 23.
Name the type of quadrilateral formedby the following points and give reasons for your answer :
(i) (-1, -2), (1, 0), (-1, 2), (-3, 0)
(ii) (4, 5), (7, 6), (4, 3), (1, 2)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q23.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q23.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q23.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q23.4

Question 24.
Find the coordinates of the circumcentre of the triangle whose vertices are (8, 6), (8, -2) and (2, -2). Also, find its circumradius.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q24.1

Question 25.
If two opposite vertices of a square are (3, 4) and (1, -1), find the coordinates of the other two vertices.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q25.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q25.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry 19.4 Q25.3

Multiple Choice Questions

Choose the correct answer from the given four options (1 to 16):
Question 1.
Point (-3, 5) lies in the
(a) first quadrant
(b) second quadrant
(c) third quadrant
(d) fourth quadrant
Solution:
Point (-3, 5) lies in second quadrant, (b)

Question 2.
Point (0, -7) lies
(a) on the x-axis
(b) in the second quadrant
(c) on the y-axis
(d) the fourth quadrant
Solution:
Point (0, -7) lies on y-axis (as x = 0) (c)

Question 3.
Abscissa of a point is positive in
I and II quadrants
I and IV quadrants
I quadrant only
II quadrant only
Solution:
Abscissa of a point is positive in first and fourth quadrants. (b)

Question 4.
The point which lies ony-axis at a distance of 5 units in the negative direction of y- axis is
(a) (0, 5)
(b) (5, 0)
(c) (0, -5)
(d) (-5, 0)
Solution:
(0, -5) is the required point. (c)

Question 5.
If the perpendicular distance of a point P from the x-axis is 5 units and the foot of perpendicular lies on the negative direction of x-axis, then the point P has
(a) x-coordinate = -5
(b) y-coordinate = 5 only
(c) y-coordinate = -5 only
(d) y-coordinate = 5 or -5
Solution:
Perpendicular distance for a point P on x- axis in negative direction.
It will has y = 5 and x = -5 (d)
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q5.1

Question 6.
The points whose abscissa and ordinate have different signs will lie in
(a) I and II quadrants
(b) II and III quadrants
(c) I and III quadrants
(d) II and IV quadrants
Solution:
Point which has abscissa and ordinate having different signs will lie in second and fourth quadrants. (d)

Question 7.
The points (-5, 2) and (2, -5) lie in
(a) same quadrant
(b) II and III quadrants respectively
(c) II and IV quadrants respectively
(d) IV and II quadrants respectively
Solution:
Points (-5, 2) and (2, -5) lie in second and fourth quadrants respectively. (b)

Question 8.
If P (-1,1), Q (3, -4), R (1, -1), S (-2, -3) and T (-4, 4) are plotted on the graph paper, then point(s) in the fourth quadrant are
(a) P and T
(b) Q and R
(c) S only
(d) P and R
Solution:
Points P (-1, 1), Q (3, -4), R (1, -1), S (-2, -3) and T (-4, 4) are plotted on graph The points in 4th quadrant are Q and R (b)

Question 9.
On plotting the points O (0, 0), A (3, 0), B (3, 4), C (0, 4) and joining OA, AB, BC and CO which of the following figure is obtained?
(a) Square
(b) Rectangle
(c) Trapezium
(d) Rhombus
Solution:
On plotting the points O (0, 0), A (3, 0), B (3, 4), C (0, 4)
OA, AB, BC and CO are joined
The figure so formed will a rectangle (b)

Question 10.
Which of the following points lie on the graph of the equation :
3x-5y + 7 = 0?
(a) (1, -2)
(b) (2, 1)
(c) (-1, 2)
(d) (1, 2)
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q10.1

Question 11.
The pair of equation x – a and y = b graphically represents lines which are
(a) parallel
(b) intersecting at (b, a)
(c) coincident
(d) intersecting at (a, b)
Solution:
x = a, y = 6
Which are intersecting at (a, b) (d)

Question 12.
The distance of the point P (2, 3) from the x>axis is
(a) 2 units
(b) 3 units
(c) 1 unit
(d) 5 units
Solution:
The distance of the point P (2, 3) from x- axis is 3 units (as y = 3). (b)

Question 13.
The distance of the point P (-4, 3) from the y-axis is
(a) 5 units
(b) -4 units
(c) 4 units
(d) 3 units
Solution:
The distance of the point P (-4, 3) from y- axis will be 4 units. (c)

Question 14.
The distance of the point P (-6, 8) from the origin is
(a) 8 units
(b) 2\(\sqrt { 7 }\) units
(c) 10 units
(d) 6 units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q14.1

Question 15.
The distance between the points A (0, 6) and B (0, -2) is
(a) 6 units
(b) 8 units
(c) 4 units
(d) 2 units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q15.1

Question 16.
The distance between the points (0, 5) and (-5, 0) is
(a) 5 units
(b) 5\(\sqrt { 2 }\)units
(c) 2 \(\sqrt { 7 }\) units
(d) 10 units
Solution:
The distance between the points (0, 5) and (-5, 0) is
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q16.1

Question 17.
AOBC is a rectangle whose three vertices are A (0, 3), O (0, 0) and B (5, 0). The length of its diagonal is
(a) 5 units
(b) 3 units
(c) \(\sqrt { 34 }\) units
(d) 4 units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q17.1

Question 18.
If the distance between the points (2, -2) and (-1, x) is S units, then one of the value of x is
(a) -2
(b) 2
(c) -1
(d) 1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q18.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q18.2

Question 19.
The distance between the points (4, p) and (1, 0) is 5 units, then the value of p is
(a) 4 only
(b) -4 only
(c) ±4
(d) 0
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q19.1

Question 20.
The points (-4, 0), (4, 0) and (0, 3) are the vertices of a
(a) right triangle
(b) isosceles triangle
(c) equilateral triangle
(d) scalene triangle
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q20.1

Question 21.
The area of a square whose vertices are A (0, -2), B (3, 1), C (0, 4) and D (-3, 1) is
(a) 18 sq. units
(b) 15 sq. units
(c) \(\sqrt { 18 }\) sq. units
(d) \(\sqrt { 15 }\) sq. units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q21.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q21.2

Question 22.
In the given figure, the area of the triangle ABC is
(a) 15 sq. units
(b) 10 sq. units
(c) 7.5 sq. units
(d) 2.5 sq. units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q22.2

Question 23.
The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is
(a) 5 units
(b) 12 units
(c) 11 units
(d) 7 + \(\sqrt { 5 }\) units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q23.1

Question 24.
If A is a point on the .y-axis whose ordinate is 5 and B is the point (-3, 1), then the length of AB is
(a) 8 units
(b) 5 units
(c) 3 units
(d) 25 units
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q24.1

Question 25.
The point A (9, 0), B (9, 6), C (-9, 6) and D (-9, 0) are the vertices of a
(a) rectangle
(b) square
(c) rhombus
(d) trapezium
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry mul Q25.1

Chapter Test

Question 1.
Three vertices of a rectangle are A (2, -1), B (2, 7) and C(4, 7). Plot these points on a graph and hence use it to find the co-ordinates of the fourth vertex D Also find the co-ordinates of
(i) the mid-point of BC
(ii) the mid point of CD
(iii) the point of intersection of the diagonals. What is the area of the rectangle ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q1.1

Question 2.
Three vertices of a parallelogram are A (3, 5), B (3, -1) and C (-1, -3). Plot these points on a graph paper and hence use it to find the coordinates of the fourth vertex D. Also find the coordinates of the mid-point of the side CD. What is the area of the parallelogram?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q2.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q2.2

Question 3.
Draw the graphs of the following linear equations.
(i) y = 2x – 1
(ii) 2x + 3y = 6
(iii) 2x – 3y = 4.
Also find slope and y-intercept of these lines.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q3.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q3.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q3.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q3.4

Question 4.
Draw the graph of the equation 3x – 4y = 12. From the graph, find :
(i) the value of y when x = -4
(ii) the value of x when y = 3.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q4.2

Question 5.
Solve graphically, the simultaneous equations: 2x – 3y = 7; x + 6y = 11.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q5.2

Question 6.
Solve the following system of equations graphically: x – 2y – 4 = 0, 2x + .y – 3 = 0.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q6.2

Question 7.
Using a scale of l cm to 1 unit for both the axes, draw the graphs of the following equations : 6y = 5x:+ 10,y = 5;c-15. From the graph, find
(i) the coordinates of the point where the two lines intersect.
(ii) the area of the triangle between the lines and the x-axis.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q7.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q7.2

Question 8.
Find, graphically, the coordinates of the vertices of the triangle formed by the lines : 8y – 3x + 7 = 0, 2x-y + 4 = 0 and 5x + 4y = 29.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q8.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q8.3

Question 9.
Find graphically the coordinates of the vertices of the triangle formed by the lines y-2 = 0,2y + x = 0 and y + 1 = 3(x – 2). Hence, find the area of the triangle formed by these lines.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q9.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q9.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q9.3

Question 10.
A line segment is of length 10 units and one of its end is (-2,3). If the ordinate of the other end is 9, find the abscissa of the other end.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q10.1

Question 11.
A (-4, -1), B (-1, 2) and C (a, 5) are the vertices of an isosceles triangle. Find the value of a, given that AB is the unequal side.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q11.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q11.2

Question 12.
If A (-3, 2), B (a, p) and C (-1, 4) are the vertices of an isosceles triangle, prove that α + β = 1, given AB = BC.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q12.2

Question 13.
Prove that the points (3, 0), (6, 4) and (-1, 3) are the vertices of a right angled isosceles triangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q13.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q13.2

Question 14.
(i) Show that the points (2, 1), (0,3), (-2, 1) and (0, -1), taken in order, are the vertices of a square. Also find the area of the square.
(ii) Show that the points (-3, 2), (-5, -5), (2, -3) and (4, 4), taken in order, are the vertices of rhombus. Also find its area. Do the given points form a square?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q14.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q14.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q14.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q14.4

Question 15.
The ends of a diagonal of a square have co-ordinates (-2, p) and (p, 2). Find p if the area of the square is 40 sq. units.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q15.1

Question 16.
What type of quadrilateral do the points A (2, -2), B (7, 3), C (11, -1) and D (6, -6), taken in the order, form?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q16.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q16.2

Question 17.
Find the coordinates of the centre of the circle passing through the three given points A (5, 1), B (-3, -7) and C (7, -1).
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q17.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q17.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 19 Coordinate Geometry ch Q17.3

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem

Question 1.
(a) In the figure (1) given below, D, E and F are mid-points of the sides BC, CA and AB respectively of ∆ ABC. If AB = 6 cm, BC = 4.8 cm and CA= 5.6 cm, find the perimeter of (i) the trapezium FBCE (ii) the triangle DEF.
(b) In the figure (2) given below, D and E are mid-points of the sides AB and AC respectively. If BC =
5.6 cm and∠B = 72°, compute (i) DE (ii)∠ADE.
(c) In the figure (3) given below, D and E are mid-points of AB, BC respectively and DF || BC. Prove that DBEF is a parallelogram. Calculate AC if AF = 2.6 cm.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q1.1
Solution:
(a) (i) Given : AB = 6 cm, BC = 4.8 cm, and CA = 5.6 cm
Required : The perimeter of trapezium FBCA.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q1.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q1.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q1.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q1.5

Question 2.
Prove that the four triangles formed by joining in pairs the mid-points of the sides c of a triangle are congruent to each other.
Solution:
Given: In ∆ ABC, D, E and r,
F are mid-points of AB, BC and CA respectively. Join DE, EF and FD.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q2.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q2.2

Question 3.
If D, E and F are mid-points of sides AB, BC and CA respectively of an isosceles triangle ABC, prove that ∆DEF is also F, isosceles.
Solution:
Given : ABC is an isosceles triangle in which AB = AC
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q3.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q3.2

Question 4.
The diagonals AC and BD of a parallelogram ABCD intersect at O. If P is the mid-point of AD, prove that
(i) PQ || AB
(ii) PO=\(\frac { 1 }{ 2 }\)CD.
Solution:
(i) Given : ABCD is a parallelogram in which diagonals AC and BD intersect each other. At point O, P is the mid-point of AD. Join OP.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q4.2

Question 5.
In the adjoining figure, ABCD is a quadrilateral in which P, Q, R and S are mid-points of AB, BC, CD and DA respectively. AC is its diagonal. Show that
(i) SR || AC and SR =\(\frac { 1 }{ 2 }\)AC
(ii) PQ = SR
(iii) PQRS is a parallelogram.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q5.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q5.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q5.3

Question 6.
Show that the quadrilateral formed by joining the mid-points of the adjacent sides of a square, is also a square,
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q6.2

Question 7.
In the adjoining figure, AD and BE are medians of ∆ABC. If DF U BE, prove that CF = \(\frac { 1 }{ 4 }\) AC.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q7.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q7.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q7.3

Question 8.
(a) In the figure (1) given below, ABCD is a parallelogram. E and F are mid-points of the sides AB and CO respectively. The straight lines AF and BF meet the straight lines ED and EC in points G and H respectively. Prove that
(i) ∆HEB = ∆HCF
(ii) GEHF is a parallelogram.
(b) In the diagram (2) given below, ABCD is a parallelogram. E is mid-point of CD and P is a point on AC such that PC = \(\frac { 1 }{ 4 }\) AC. EP produced meets BC at F. Prove that
(i) F is mid-point of BC (ii) 2EF = BD
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q8.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q8.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q8.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q8.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q8.5

Question 9.
ABC is an isosceles triangle with AB = AC. D, E and F are mid-points of the sides BC, AB and AC respectively. Prove that the line segment AD is perpendicular to EF and is bisected by it.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q9.1

Question 10.
(a) In the quadrilateral (1) given below, AB || DC, E and F are mid-points of AD and BD respectively. Prove that:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q10.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q10.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q10.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q10.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q10.5

Question 11.
(a) In the quadrilateral (1) given below, AD = BC, P, Q, R and S are mid-points of AB, BD, CD and AC respectively. Prove that PQRS is a rhombus.
(b) In the figure (2) given below, ABCD is a kite in which BC = CD, AB = AD, E, F, G are mid-points of CD, BC and AB respectively. Prove that:
(i) ∠EFG = 90
(ii) The line drawn through G and parallel to FE bisects DA.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q11.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q11.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q11.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q11.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q11.5

Question 12.
In the adjoining figure, the lines l, m and n are parallel to each other, and G is mid-point of CD. Calculate:
(i) BG if AD = 6 cm
(ii) CF if GE = 2.3 cm
(iii) AB if BC = 2.4 cm
(iv) ED if FD = 4.4 cm.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q12.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q12.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem Q12.3

Multiple Choice Questions

Choose the correct answer from the given four options (1 to 6):
Question 1.
In a ∆ABC, AB = 3 cm, BC = 4 cm and CA = 5 cm. IfD and E are mid-points of AB and BC respectively, then the length of DE is
(a) 1.5 cm
(b) 2 cm
(c) 2.5 cm
(d) 3.5 cm
Solution:
In ∆ABC, D and E are the mid-points of sides AB and BC
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem mul Q1.1

Question 2.
In the given figure, ABCD is a rectangle in which AB = 6 cm and AD = 8 cm. If P and Q are mid-points of the sides BC and CD respectively, then the length of PQ is
(a) 7 cm
(b) 5 cm
(c) 4 cm
(d) 3 cm
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem mul Q2.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem mul Q2.2

Question 3.
D and E are mid-points of the sides AB and AC of ∆ABC and O is any point on the side BC. O is joined to A. If P and Q are mid-points of OB and OC respectively, then DEQP is
(a) a square
(b) a rectangle
(c) a rhombus
(d) a parallelogram
Solution:
D and E are mid-points of sides AB and AC respectively of AABC O is any point on BC and AO is joined P and Q are mid-points of OB and OC, EQ and DP are joined
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem mul Q3.1

Question 4.
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectanlge if
(a) PQRS is a parallelogram
(b) PQRS is a rectangle
(c) the diagonals of PQRS are perpendicular to each other
(d) the diagonals of PQRS are equal.
Solution:
A, B, C and D are the mid-points of the sides PQ, QR, RS and SP respectively
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem mul Q4.1

Question 5.
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a rhombus if
(a) ABCD is a parallelogram
(b) ABCD is a rhombus
(c) the diagonals of ABCD are equal
(d) the diagonals of ABCD are perpendicular to each other.
Solution:
P, Q, R and S are the mid-points of the quadrilateral ABCD and a quadrilateral is formed by joining the mid-points in order
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem mul Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem mul Q5.2

Question 6.
The figure formed by joining the mid points of the sides of a quadrilateral
ABCD, taken in order, is a square only if
(a) ABCD is a rhombus r
(b) diagonals of ABCD are equal
(c) diagonals of ABCD are perpendicular to each other
(d) diagonals of ABCD are equal and perpendicular to each other.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem mul Q6.1

Chapter Test

Question 1.
ABCD is a rhombus with P, Q and R as midpoints of AB, BC and CD respectively. Prove that PQ ⊥ QR.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem ch Q1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem ch Q1.2

Question 2.
The diagonals of a quadrilateral ABCD are perpendicular. Show that the quadrilateral formed by joining the mid-points of its adjacent sides is a rectangle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem ch Q2.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem ch Q2.2

Question 3.
If D, E, F are mid-points of the sides BC, CA and AB respectively of a ∆ ABC, Prove that AD and FE bisect each other.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem ch Q3.1

Question 4.
In ∆ABC, D and E are mid-points of the sides AB and AC respectively. Through E, a straight line is drawn parallel to AB to meet BC at F. Prove that BDEF is a parallelogram. If AB = 8 cm and BC = 9 cm, find the perimeter of the parallelogram BDEF.
Solution:
In ∆ABC, D and E are the mid-points of
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem ch Q4.1

Question 5.
In the given figure, ABCD is a parallelogram and E is mid-point of AD. DL EB meets AB produced at F. Prove that B is mid-point of AF and EB = LF.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem ch Q5.1
Solution:
Given In the figure
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem ch Q5.2

Question 6.
In the given figure, ABCD is a parallelogram. If P and Q are mid-points of sides CD and BC respectively. Show that CR = \(\frac { 1 }{ 2 }\) AC.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem ch Q6.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 11 Mid Point Theorem ch Q6.2

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures

ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures

Exercise 13.1

Question 1.
If two angles of a quadrilateral are 40° and 110° and the other two are in the ratio 3 : 4, find these angles.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q1.1

Question 2.
If the angles of a quadrilateral, taken in order, are in the ratio 1 : 2 : 3 : 4, prove that it is a trapezium.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q2.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q2.2

Question 3.
If an angle of a parallelogram is two-thirds of its adjacent angle, find the angles of the parallelogram.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q3.1

Question 4.
(a) In figure (1) given below, ABCD is a parallelogram in which ∠DAB = 70°, ∠DBC = 80°. Calculate angles CDB and ADB.
(b) In figure (2) given below, ABCD is a parallelogram. Find the angles of the AAOD.
(c) In figure (3) given below, ABCD is a rhombus. Find the value of x.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q4.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q4.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q4.3

Question 5.
(a) In figure (1) given below, ABCD is a parallelogram with perimeter 40. Find the values of x and y.
(b) In figure (2) given below. ABCD is a parallelogram. Find the values of x and y.
(c) In figure (3) given below. ABCD is a rhombus. Find x and y.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q5.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q5.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q5.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q5.4

Question 6.
The diagonals AC and BD of a rectangle > ABCD intersect each other at P. If ∠ABD = 50°, find ∠DPC.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q6.1

Question 7.
(a) In figure (1) given below, equilateral triangle EBC surmounts square ABCD. Find angle BED represented by x.
(b) In figure (2) given below, ABCD is a rectangle and diagonals intersect at O. AC is produced to E. If ∠ECD = 146°, find the angles of the ∆ AOB.
(c) In figure (3) given below, ABCD is rhombus and diagonals intersect at O. If ∠OAB : ∠OBA = 3:2, find the angles of the ∆ AOD.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q7.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q7.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q7.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q7.4

Question 8.
(a) In figure (1) given below, ABCD is a trapezium. Find the values of x and y.
(b) In figure (2) given below, ABCD is an isosceles trapezium. Find the values of x and.y.
(c) In figure (3) given below, ABCD is a kite and diagonals intersect at O. If ∠DAB = 112° and ∠DCB = 64°, find ∠ODC and ∠OBA.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q8.2
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q8.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q8.4

Question 9.
(i) Prove that each angle of a rectangle is 90°.
(ii) If the angle of a quadrilateral are equal, prove that it is a rectangle.
(iii) If the diagonals of a rhombus are equal, prove that it is a square.
(iv) Prove that every diagonal of a rhombus bisects the angles at the vertices.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q9.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q9.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q9.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q9.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q9.5

Question 10.
ABCD is a parallelogram. If the diagonal AC bisects ∠A, then prove that:
(i) AC bisects ∠C
(ii) ABCD is a rhombus
(iii) AC ⊥ BD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q10.1

Question 11.
(i) Prove that bisectors of any two adjacent angles of a parallelogram are at right angles.
(ii) Prove that bisectors of any two opposite angles of a parallelogram are parallel.
(iii) If the diagonals of a quadrilateral are equal and bisect each other at right angles, then prove that it is a square.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.5
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q11.6

Question 12.
(i) If ABCD is a rectangle in which the diagonal BD bisect ∠B, then show that ABCD is a square.
(ii) Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q12.2

Question 13.
P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q13.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q13.2

Question 14.
(a) In figure (1) given below, ABCD is a parallelogram and X is mid-point of BC. The line AX produced meets DC produced at Q. The parallelogram ABPQ is completed. Prove that:
(i) the triangles ABX and QCX are congruent;
(ii)DC = CQ = QP
(b) In figure (2) given below, points P and Q have been taken on opposite sides AB and CD respectively of a parallelogram ABCD such that AP = CQ. Show that AC and PQ bisect each other.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q14.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q14.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q14.3

Question 15.
ABCD is a square. A is joined to a point P on BC and D is joined to a point Q on AB. If AP=DQ, prove that AP and DQ are perpendicular to each other.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q15.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q15.2

Question 16.
If P and Q are points of trisection of the diagonal BD of a parallelogram ABCD, prove that CQ || AP.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q16.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q16.2

Question 17.
A transversal cuts two parallel lines at A and B. The two interior angles at A are bisected and so are the two interior angles at B ; the four bisectors form a quadrilateral ABCD. Prove that
(i) ABCD is a rectangle.
(ii) CD is parallel to the original parallel lines.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.5
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.6
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q17.7

Question 18.
In a parallelogram ABCD, the bisector of ∠A meets DC in E and AB = 2 AD. Prove that
(i) BE bisects ∠B
(ii) ∠AEB = a right angle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q18.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q18.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q18.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q18.4

Question 19.
ABCD is a parallelogram, bisectors of angles A and B meet at E which lie on DC. Prove that AB
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q19.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q19.2

Question 20.
ABCD is a square and the diagonals intersect at O. If P is a point on AB such that AO =AP, prove that 3 ∠POB = ∠AOP.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q20.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q20.2

Question 21.
ABCD is a square. E, F, G and H are points on the sides AB, BC, CD and DA respectively such that AE = BF = CG = DH. Prove that EFGH is a square.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q21.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q21.2

Question 22.
(a) In the Figure (1) given below, ABCD and ABEF are parallelograms. Prove that
(i) CDFE is a parallelogram
(ii) FD = EC
(iii) Δ AFD = ΔBEC.
(b) In the figure (2) given below, ABCD is a parallelogram, ADEF and AGHB are two squares. Prove that FG = AC
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q22.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q22.3

Question 23.
ABCD is a rhombus in which ∠A = 60°. Find the ratio AC : BD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q23.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures Q23.2

Exercise 13.2

Question 1.
Using ruler and compasses only, construct the quadrilateral ABCD in which ∠ BAD = 45°, AD = AB = 6cm, BC = 3.6cm, CD = 5cm. Measure ∠ BCD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q1.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q1.2

Question 2.
Draw a quadrilateral ABCD with AB = 6cm, BC = 4cm, CD = 4 cm and ∠ ABC = ∠ BCD = 90°
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q2.1

Question 3.
Using ruler and compasses only, construct the quadrilateral ABCD given that AB = 5 cm, BC = 2.5 cm, CD = 6 cm, ∠BAD = 90° and the diagonal AC = 5.5 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q3.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q3.2

Question 4.
Construct a quadrilateral ABCD in which AB = 3.3 cm, BC = 4.9 cm, CD = 5.8 cm, DA = 4 cm and BD = 5.3 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q4.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q4.2

Question 5.
Construct a trapezium ABCD in which AD || BC, AB = CD = 3 cm, BC = 5.2cm and AD = 4 cm
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q5.1

Question 6.
Construct a trapezium ABCD in which AD || BC, ∠B= 60°, AB = 5 cm. BC = 6.2 cm and CD = 4.8 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q6.2

Question 7.
Using ruler and compasses only, construct a parallelogram ABCD with AB = 5.1 cm, BC = 7 cm and ∠ABC = 75°.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q7.1

Question 8.
Using ruler and compasses only, construct a parallelogram ABCD in which AB = 4.6 cm, BC = 3.2 cm and AC = 6.1 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q8.1

Question 9.
Using ruler and compasses, construct a parallelogram ABCD give that AB = 4 cm, AC = 10 cm, BD = 6 cm. Measure BC.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q9.1

Question 10.
Using ruler and compasses only, construct a parallelogram ABCD such that BC = 4 cm, diagonal AC = 8.6 cm and diagonal BD = 4.4 cm. Measure the side AB.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q10.1

Question 11.
Use ruler and compasses to construct a parallelogram with diagonals 6 cm and 8 cm in length having given the acute angle between them is 60°. Measure one of the longer sides.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q11.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q11.2

Question 12.
Using ruler and compasses only, draw a parallelogram whose diagonals are 4 cm and 6 cm long and contain an angle of 75°. Measure and write down the length of one of the shorter sides of the parallelogram.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q12.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q12.2

Question 13.
Using ruler and compasses only, construct a parallelogram ABCD with AB = 6 cm, altitude = 3.5 cm and side BC = 4 cm. Measure the acute angles of the parallelogram.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q13.1

Question 14.
The perpendicular distances between the pairs of opposite sides of a parallelogram ABCD are 3 cm and 4 cm and one of its angles measures 60°. Using ruler and compasses only, construct ABCD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q14.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q14.2

Question 15.
Using ruler and compasses, construct a rectangle ABCD with AB = 5cm and AD = 3 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q15.1

Question 16.
Using ruler and compasses only, construct a rectangle each of whose diagonals measures 6cm and the diagonals intersect at an angle of 45°.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q16.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q16.2

Question 17.
Using ruler and compasses only, construct a square having a diagonal of length 5cm. Measure its sides correct to the nearest millimeter.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q17.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q17.2

Question 18.
Using ruler and compasses only construct A rhombus ABCD given that AB 5cm, AC = 6cm measure ∠BAD.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q18.1

Question 19.
Using ruler and compasses only, construct rhombus ABCD with sides of length 4cm and diagonal AC of length 5 cm. Measure ∠ABC.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q19.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q19.2

Question 20.
Construct a rhombus PQRS whose diagonals PR and QS are 8cip and 6cm respectively.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q20.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q20.2

Question 21.
Construct a rhombus ABCD of side 4.6 cm and ∠BCD = 135°, by using ruler and compasses only.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q21.1

Question 22.
Construct a trapezium in which AB || CD, AB = 4.6 cm, ∠ ABC = 90°, ∠ DAB = 120° and the distance between parallel sides is 2.9 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q22.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q22.2

Question 23.
Construct a trapezium ABCD when one of parallel sides AB = 4.8 cm, height = 2.6cm, BC = 3.1 cm and AD = 3.6 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q23.1

Question 24.
Construct a regular hexagon of side 2.5 cm.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q24.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 Q24.2

Multiple Choice Questions

Choose the correct answer from the given four options (1 to 12):
Question 1.
Three angles of a quadrilateral are 75°, 90° and 75°. The fourth angle is
(a) 90°
(b) 95°
(c) 105°
(d) 120°
Solution:
Sum of 4 angles of a quadrilateral = 360° Sum of three angles = 75° + 90° + 75° = 240° Fourth angle = 360° – 240° = 120° (d)

Question 2.
A quadrilateral ABCD is a trapezium if
(a) AB = DC
(b) AD = BC
(c) ∠A + ∠C = 180°
(d) ∠B + ∠C = 180°
Solution:
A quadrilateral ABCD is a trapezium if ∠B + ∠C= 180°
(Sum of co-interior angles) (d)

Question 3.
If PQRS is a parallelogram, then ∠Q – ∠S is equal to
(a) 90°
(b) 120°
(c) 0°
(d) 180°
Solution:
PQRS is a parallelogram ∠Q – ∠S = 0
(∵ Opposite angles of a parallelogram, are equal) (c)

Question 4.
A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is
(a) 55°
(b) 50°
(c) 40°
(d) 25°
Solution:
In a rectangle a diagonal is inclined to one side of the rectangle is 25°
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures mul Q4.1

Question 5.
ABCD is a rhombus such that ∠ACB = 40°. Then ∠ADB is
(a) 40°
(b) 45°
(c) 50°
(d) 60°
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures mul Q5.1

Question 6.
The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠D AC = 32° and ∠AOB = 70°, then ∠DBC is equal to
(a) 24°
(b) 86°
(c) 38°
(d) 32°
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures mul Q6.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures mul Q6.2

Question 7.
If the diagonals of a square ABCD intersect each other at O, then ∆OAB is
(a) an equilateral triangle
(b) a right angled but not an isosceles triangle
(c) an isosceles but not right angled triangle
(d) an isosceles right angled triangle
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures mul Q7.1

Question 8.
If the diagonals of a quadrilateral PQRS bisect each other, then the quadrilateral PQRS must be a
(a) parallelogram
(b) rhombus
(c) rectangle
(d) square
Solution:
Diagonals of a quadrilateral PQRS bisect each other, then quadrilateral must be a parallelogram.
(∵ A rhombus, rectangle and square are also parallelogram) (a)

Question 9.
If the diagonals of a quadrilateral PQRS bisect each other at right angles, then the quadrilateral PQRS must be a
(a) parallelogram
(b) rectangle
(c) rhombus
(d) square
Solution:
Diagonals of quadrilateral PQRS bisect each other at right angles, then quadrilateral PQRS [ must be a rhombus.
(∵ Square is also a rhombus with each angle equal to 90°) (c)

Question 10.
Which of the following statement is true for a parallelogram?
(a) Its diagonals are equal.
(b) Its diagonals are perpendicular to each other.
(c) The diagonals divide the parallelogram into four congruent triangles.
(d) The diagonals bisect each other.
Solution:
For a parallelogram an the statement ‘The diagoanls bisect each other’ is true. (d)

Question 11.
Which of the following is not true for a parallelogram?
(a) opposite sides are equal
(b) opposite angles are equal
(c) opposite angles are bisected by the diagonals
(d) diagonals bisect each other
Solution:
The statement that in a parallelogram, .the opposite angles are bisected by the diagonals, is not true in each case. (c)

Question 12.
A quadrilateral in which the diagonals are equal and bisect each other at right angles is a
(a) rectangle which is not a square
(b) rhombus which is not a square
(c) kite which is not a square
(d) square
Solution:
In a quadrilateral, if diagonals are equal and bisect each other at right angles, is a square. (d)

Chapter Test

Question P.Q.
The interior angles of a polygon add upto 4320°. How many sides does the polygon have ?
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures ch Qp1.1

Question P.Q.
If the ratio of an interior angle to the exterior angle of a regular polygon is 5:1, find the number of sides.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures ch Qp1.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures ch Q1.3

Question P.Q.
In a pentagon ABCDE, BC || ED and ∠B: ∠A : ∠E =3:4:5. Find ∠A.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures ch Q3.1

Question 1.
In the given figure, ABCD is a parallelogram. CB is produced to E such that BE=BC. Prove that AEBD is a parallelogram.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures p.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures p.2

Question 2.
In the given figure, ABC is an isosceles triangle in which AB=AC. AD bisects exterior angle PAC and CD || BA. Show that
(i) ∠DAC=∠BCA
(ii) ABCD is a parallelogram.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures p.3

Question 3.
Prove that the quadrilateral obtained by joining the mid-points of an isosceles trapezium is a rhombus.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 13.2 p.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures p.5

Question 4.
Find the size of each lettered angle in the Following Figures.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 4.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 4.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 4.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 4.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 4.5

Question 5.
Find the size of each lettered angle in the following figures :
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 5.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 5.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 5.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 5.4
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 5.5

Question 6.
In the adjoining figure, ABCD is a rhombus and DCFE is a square. If ∠ABC = 56°, find
(i) ∠DAG
(ii) ∠FEG
(iii) ∠GAC
(iv) ∠AGC.
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 6.1
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 6.2
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 6.3
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 6.4

Question 7.
If one angle of a rhombus is 60° and the length of a side is 8 cm, find the lengths of its diagonals.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 7.1

Question 8.
Using ruler and compasses only, construct a parallelogram ABCD with AB = 5 cm, AD = 2.5 cm and ∠BAD = 45°. If the bisector of ∠BAD meets DC at E, prove that ∠AEB is a right angle.
Solution:
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 8.1
ML Aggarwal Class 9 Solutions for ICSE Maths Chapter 13 Rectilinear Figures 8.2

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 25 Value Added Tax Chapter Test

ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 25 Value Added Tax Chapter Test

These Solutions are part of ML Aggarwal Class 10 Solutions for ICSE Maths. Here we have given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 1 Value Added Tax Chapter Test.

ML Aggarwal SolutionsICSE SolutionsSelina ICSE Solutions

Question 1.
A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being ₹ 18000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax is 8%, find:
(i) the VAT paid by the shopkeeper. 
(ii) the total amount that the consumer pays for the washing machine.
Solution:
(i) SP of washing machine
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 25 Value Added Tax Chapter Test Q50.1
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 25 Value Added Tax Chapter Test Q50.2

Question 2.
A manufacturing company sold an article to its distributor for ₹22000 including VAT. The distributor sold the article to a dealer for ₹22000 excluding tax and the dealer sold it to a consumer for ₹25000 plus tax (under VAT). If the rate of sales tax (under VAT) at each stage is 10%, find :
(i) the sale price of the article for the manufacturing company.
(ii) the amount of VAT paid by the dealer.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 25 Value Added Tax Chapter Test Q50.3

Question 3.
The marked price of an article is ₹7500. A shopkeeper sells the article to a consumer at the marked prices and charges sales tax at . the rate of 7%. If the shopkeeper pays a VAT of ₹105, find the price inclusive of sales tax of the article which the shopkeeper paid to the wholesaler.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 25 Value Added Tax Chapter Test Q50.4

Question 4.
A shopkeeper buys an article at a discount of 30% and pays sales tax at the rate of 6%. The shopkeeper sells the article to a consumer at 10% discount on the list price and charges sales tax at the’ same rate. If the list price of the article is ₹3000, find the price inclusive of sales tax paid by the shopkeeper.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 25 Value Added Tax Chapter Test Q50.5

Question 5.
Mukerjee purchased a movie camera for ₹27468. which includes 10% rebate on the list price and then 9% sales tax (under VAT) on the remaining price. Find the list price of the movie camera.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 25 Value Added Tax Chapter Test Q50.6

Question 6.
A retailer buys an article at a discount of 15% on the printed price from a wholesaler. He marks up the price by 10%. Due to competition in the market, he allows a discount of 5% to a buyer. If the buyer pays ₹451.44 for the article inclusive of sales tax (under VAT) at 8%, find :
(i) the printed price of the article
(ii) the profit percentage of the retailer.
Solution:
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 25 Value Added Tax Chapter Test Q50.7
ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 25 Value Added Tax Chapter Test Q50.8

Hope given ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 1 Value Added Tax Chapter Test are helpful to complete your math homework.

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