How Do You Find The Perimeter Of A Polygon? - A Plus Topper

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.