## How do you find the Perimeter of a Polygon?

**Polygon**

A polygon is a simple closed figure that consist of line segments only. Thus, a polygon is a closed rectilinear figure.

The following figures are examples of polygons :

**Regular polygon**

A regular polygon is a polygon in which all the sides are equal.

### Perimeter of a Polygon

The sum of the length of all sides of a closed figure is called the **perimeter** of the figure.

Perimeter of some polygons are given in the table below :

Figure | Name of the figure | Perimeter |

Scalene Triangle | (a + b + c) Sum of the length of sides | |

Isosceles Triangle | (2a + b) 2 × Length of equal sides + Length of unequal side | |

Equilateral Triangle | 3a 3 × Length of the side of triangle | |

Rectangle | 2(a + b) 2 (Sum of the length and breadth) | |

Parallelogram | 2(a + b) 2 (Length + breadth) | |

Square | 4a 4 × Length of the side of square | |

Rhombus | 4a 4 × Length of the side of rhombus |

**Note :**

The perimeter of a regular polygon = Number of sides × Length of one side.

### Perimeter of a Polygon Problems with Solutions

**1. Find the perimeter of the following closed figure : **

**Solution: **

(i) Perimeter of quadrilateral ABCD

= AB + BC + CD + DA

= 15 cm + 7 cm + 9 cm + 12 cm = 43 cm

(ii) Perimeter of the triangle ABC

= AB + BC + CA

= 8 cm + 10 cm + 6 cm = 24 cm

(iii) Perimeter of a square

= 4 × length of a side

= 4 × 5 cm = 20 cm.

(iv) Perimeter of a parallelogram

= 2 (length + breadth)

= 2 (6 cm + 5 cm)

= 22 cm.

**2. Find the perimeter of the following figures and identify which figure has the greater perimeter?**

**Solution:**

Perimeter of figure A, which is a square of side 8 cm = 4 × 8 cm = 32 cm.

Similarly the perimeter of figure B, which is not a square, because two square pieces of side 1 cm are cut off along one side of the square

= 8 cm + 8 cm + (8 cm + 1 cm + 1 cm + 1 cm + 1 cm) + 8 cm = 36 cm.

Clearly, figure B has the greater perimeter than figure A.

Note : When a shape is cut off from a given shape then the perimeter of the new shape so obtained is increased.

**3. Nisha wants to fence the rectangular garden in front of her house. Its length is 6 m and breadth is 3 m. The side which is not to be fenced is 6 m in length. Find the cost of fencing at the rate of ₹ 275 per m.**

**Solution:**

The garden is in shape of a rectangle. Its one of the sides (6 m) is not to be fenced. Therefore, the length of fence required is the perimeter of the garden excluding one side.

= 6 m + 3 m + 3 m

= 12 m

The cost of fencing at the rate of ₹ 275 per meter.

= ₹ 275 × 12

= ₹ 3300.