Page 224 - ICSE Math 6

Perimeter of square PQRS = PQ + QR + RS + SP

= PQ + PQ + PQ + PQ { PQ = QR= RS = SP}
= 4 × PQ = 4 × (length of a side) Maths Info
Thus, if the length of a side of a square is a units, then its perimeter
(P) is given by the formula P = 4 × a. The perimeter of a regular
polygon is the measure of one
Example 7: Find the perimeter of a square with side length 7 cm. side multiplied by the number
of sides.
Solution: Length of each side of the square = 7 cm
\ Perimeter of square = 4 × 7 cm = 28 cm

Example 8: A piece of string is 36 cm long. What is the length of each side if the string is used to
form a square?

Solution: Perimeter of a square = 4 × Side = 4 × a
Perimeter 36
∴ Side of a square (a) = = = 9 cm
4 4
Example 9: Aditya runs around a square park of side 50 m three times. Shweta runs twice around
a rectangular park of length 100 m and breadth 60 m. Who covers more distance?

Solution: Perimeter of square park = 4 × Side
= 4 × 50 m = 200 m

Distance covered by Aditya = 3 × 200 m = 600 m

Perimeter of rectangular park = 2(Length + Breadth)
= 2(100 + 60) m = 2(160) m = 320 m

Distance covered by Shweta = 2 × 320 = 640 m
Since 640 > 600, Shweta covers more distance.

Perimeter of a triangle
A triangle is a three-sided closed figure. The perimeter of a triangle is the sum of its side lengths.
If we have an equilateral DABC, then
AB = BC = CA and ∠A = ∠B = ∠C = 60°

\ Perimeter of DABC = AB + BC + CA A
= AB + AB + AB = 3 × AB 60°
= 3 × (length of a side)
Thus, if the length of a side of an equilateral triangle is a units, then its perimeter B 60° 60° C
(P) is given by the formula P = 3 × a. a

Example 10: Find the perimeter of a triangle with the side lengths 4 cm, 3 cm and 5 cm.
Solution: Perimeter of triangle = 4 cm + 3 cm + 5 cm = 12 cm

Example 11: Find the perimeter of an equilateral triangle with side length 8 m.
Perimeter of equilateral triangle = 3 × (length of a side)
= 3 × 8 m = 24 m

208