Perimeter

Selina Concise Mathematics Class 9 ICSE Solutions Area and Perimeter of Plane Figures

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Selina Concise Mathematics Class 9 ICSE Solutions Area and Perimeter of Plane Figures

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APlusTopper.com provides step by step solutions for Selina Concise Mathematics Class 9 ICSE Solutions Chapter 20 Area and Perimeter of Plane Figures. You can download the Selina Concise Mathematics ICSE Solutions for Class 9 with Free PDF download option. Selina Publishers Concise Mathematics for Class 9 ICSE Solutions all questions are solved and explained by expert mathematic teachers as per ICSE board guidelines.

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Selina ICSE Solutions for Class 9 Maths Chapter 20 Area and Perimeter of Plane Figures

Exercise 20(A)

Solution 1:
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Solution 2:
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Solution 3:
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Solution 4:
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Solution 5:
Since the perimeter of the isosceles triangle is 36cm and base is 16cm.
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Solution 11:
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Exercise 20(B)

Solution 1:
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Solution 2:
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Solution 12:
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Solution 13:
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We need to find the cost of carpeting of 80 cm = 0.8 m wide carpet, if the rate of carpeting is Rs. 25. Per metre.
Then
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Solution 20:
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In the given figure, we can observe that the non-parallel sides are equal and hence it is an isosceles trapezium.
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Exercise 20(C)

Solution 1:
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Solution 2:
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Solution 3:
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Solution 9:
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Solution 19:
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Solution 20:
From the given data, we can calculate the area of the outer circle and then the area of inner circle and hence the width of the shaded portion.
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Perimeter and Circumference

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Perimeter and Circumference

Perimeter is the word used to describe the distance around the outside of a figure.
To find the perimeter, add together the lengths of all of the sides of the figure.

Perimeter and Circumference 2

Refresh your polygon memories:

When working with perimeter, references may be made to the names of polygons. Listed at the left are some of the more common polygons whose names you should know.
Remember that “regular polygons” are polygons whose sides are all the same length and whose angles are all the same size. Not all polygons are “regular”.

Circumference is the word used to describe the distance around the outside of a circle.
Like perimeter, the circumference is the distance round the outside of the figure. Unlike perimeter, in a circle there are no straight segments to measure, so a special formula is needed
Perimeter and Circumference 1

Example 1: Ed and Carol are jogging around a circular track in the park. The diameter of the track is 0.8 miles. Find, to the nearest mile, the number of miles they jogged if they made two complete trips around the track.
Solution: C = πd
= (3.141592654)(0.8) = 2.513274123 miles (one trip)
2(2.513274123) = 5.026548246 = 5 miles

Example 2: For an art project at school, you need a piece of string long enough to wrap around the outer edge of this starfish. What is the shortest possible length for the string?
Solution:
Perimeter = 2 + 1.5 + 1 + 2 + 1.5 + 2 + 2 + 3 + 2.5 + 2
= 19.5 inches

 

How Do You Get The Perimeter Of A Shape

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How Do You Get The Perimeter Of A Shape

Rohan and his father are watching their garden. They want to fence it with barbed wire to make it safe. Before going to the market to purchase the wire, his father wants to know the length of the wire needed. To measure the length, he starts from a point on the boundary of the garden and keeps moving the measuring tape along the boundary line and reaches the initial point. That means he has made a complete round of the garden and the length of the measuring tape is equal to the distance covered in one full round. This length of the tape is the perimeter of the garden.

perimeter

PERIMETER
Perimeter of a closed figure is the total length of its boundary.
We know that all polygons (triangle, square, rectangle, pentagon, hexagon, etc) are rectilinear figures.
∴ Perimeter = Sum of the lengths of its all sides

Perimeter of a triangle

Perimeter of a triangle ABC is the sum of the lengths of its sides. If the lengths of the sides of a triangle are a, b, and c, then
Perimeter = AB + BC + CA
= c + a + b = a + b + c
Perimeter-of-triangle

Perimeter of a square

The perimeter of a square ABCD is the total lengths of its all equal sides. If the length of each side is s then,
Perimeter = AB + BC + CD + DA
= s + s + s + s = 4s
Perimeter-of-square

Perimeter of a rectangle

The perimeter of a rectangle ABCD is the double of the sum of its two adjacent sides. If the lengths of its two adjacent sides are l and b, then,
Perimeter = AB + BC + CD + DA
= l + b + l + b
= 2l + 2b
= 2(l + b)
Perimeter-of-rectangle

Shapes of different kinds with the same perimeter

We can have different kinds of shapes with the same perimeter. To understand this, let us take a string 32 cm long. What figures can we make by using this string?
Perimeter-of-triangle-1 We can make an isosceles triangle of side 10 cm, 10 cm, and 12 cm.
∴ P = AB + BC + CA
= 10 cm + 10 cm + 12 cm = 32 cm

By using a 32 cm string, we can make a square of side 8 cm.
Perimeter-of-square-1P = AB + BC + CD + DA
= 8 cm + 8 cm + 8 cm + 8 cm
= 4 × 8 cm = 32 cm

By using the same string, we can make a rectangle of length 10 cm and breadth 6 cm.
Perimeter-of-square-2P = AB + BC + CD + DA
= 6 cm + 10 cm + 6 cm + 10 cm = 32 cm

We see that in all the three cases, the perimeter is 32 cm but they have different shapes. Hence we can conclude that different kinds of shapes can have the same perimeter.

Example 1: Find the perimeter of a rectangular plot whose length is 15 m and breadth is 850 cm. Solution: Length of the rectangle = 15 m
Perimeter-of-square-3Breadth of the rectangle = 850 cm
= 850/100 m   (1 m = 100 cm)
= 8.5 m
∴ Perimeter of the rectangular plot = 2 (Length + Breadth)
= 2 (l + b)
= 2 (15 + 8.5)
= 2 × 23.5 = 47.0 m

Example 2: Find the perimeter of the given figure.
Perimeter-of-square-4
Solution: Perimeter
= AB + BC + CD + DE + EF + FG + GA
= 3.2 cm + 1.5 cm + 5 cm + 5 cm + 1.5 cm + 3.2 cm + 2 cm
= 21.4 cm

Example 3: Find the length of a string used to make a triangle ABC. If the same string is used to make a square, what will be the side of the square?
Perimeter-of-triangle-2
Solution: Perimeter of triangle ABC
= Length of the string = AB + BC + CA
= 6 cm + 12 cm + 10 cm 28 cm
Now, the same string is used to make a square. So the perimeter of a square will be 28 cm.
Perimeter of a square
= 4 × side
28 cm = 4 × side
side = 28/4 = 7 cm
Hence, the side of a square will be 7 cm.

Example 4: The perimeter of a rectangular field is 260 m. If its length is 90 m,find its breadth.
Solution: Perimeter of a rectangle
= 2 (b + l)
260 m = 2 (b + 90 m)
260 m = 2 b + 180 m
(260 – 180) m = 2b
80 m = 2b
b =  80/2 m
b = 40 m
Hence, the breadth of the rectangular field
= 40 m.