Page 222 - ICSE Math 6

21 Perimeter and Area

Key Concepts

• Concept of Perimeter • Area of a Square and a Rectangle (Using a Squared
• Perimeter of a Rectangle, Square and Triangle Paper)
• Different Shapes with the Same Perimeter • Conversion of Units

Perimeter

The perimeter of a closed figure is the length of its boundary. As 5 cm
perimeter is a length, therefore the unit of perimeter is the same as 2 cm
the given unit of side lengths. For example, the perimeter of the 3 cm
figure given alongside is,
Perimeter = 3 cm + 6 cm + 2 cm + 5 cm 6 cm

= 16 cm

Example 1: Find the perimeter of each of the following figures.

(a) 7 cm (b) 20 cm (c) 18 cm (d) 5 cm 5 cm

3 cm 6 cm 30 cm 30 cm 18 cm 18 cm 5 cm 5 cm

5 cm
40 cm 18 cm 5 cm 5 cm

Solution: To find the perimeter, we simply add the measure of all the sides.
(a) Perimeter = (7 + 6 + 5 + 3) cm = 21 cm

(b) Perimeter = (20 + 30 + 40 + 30) cm = 120 cm
(c) Perimeter = (18 + 18 + 18 + 18) cm = 72 cm

(d) Perimeter = (5 + 5 + 5 + 5 + 5 + 5) cm = 30 cm

Perimeter of a rectangle
S R
A rectangle is a four-sided closed figure with opposite sides of
equal length and each angle of 90°. Let’s find the perimeter of the b
rectangle PQRS shown alongside.
Perimeter of rectangle PQRS = PQ + QR + RS + SP P l Q

= PQ + QR + PQ + QR { RS = PQ and SP = OR}
= 2 × PQ + 2 × QR

= 2 × (PQ + QR)
Thus, if the length and breadth of a rectangle are l units and b units respectively, then its perimeter
(P) is given by the formula P = 2 × (l + b).

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