Page 224 - ICSE Math 8

21 Perimeter and Area of Plane

Figures

Key Concepts

• Area and Perimeter of a Rectangle • Area of a Trapezium
• Area and Perimeter of a Square • Area of a Polygon
• Area of a Triangle • Area of a Circle
• Area of a Parallelogram

Perimeter of a closed plane figure is the length of its boundary. 2 4 2
As perimeter is a length therefore the unit of perimeter is same 1 m = 100 cm ¥ 100 cm = 10 cm
2
as the given unit of length. 1 m = 10 dm ¥ 10 dm = 100 dm 2
2
Area is the region enclosed inside a closed boundary. 1 dm = 10 cm ¥ 10 cm = 100 cm 2
2
2
2
A square centimetre or cm is the standard unit of area, which 1 dam = 10 m ¥ 10 m = 100 m (1 arc)
means the area of a region enclosed by a square of side 1 cm. 1 hectare = 10,000 m 2
2
Other units of the area are square metre (m ), square decimetre 1 km = 1,000 m ¥ 1,000 m = 10 m 2
2
6
2
2
(dm ), square decametre (dam ), and so on. 1 km = 100 hectare
2
In this chapter, we will revise the formulae for areas and
perimeters of rectangles, squares, triangles, parallelograms and
a trapezium. In the end, we will take up area of semicircle. Maths Info
2
1 are = 100 m . This is used as unit of measuring
area of land. Larger areas are expressed in
Area and Perimeter of a Rectangle hectares (ha).
D C
If the length of a rectangle is l units and its breadth is b units, then its area is
2
(l × b) unit .
d b
Perimeter of a rectangle = 2(l + b)
2
2
It d be the length of the diagonal AC of rectangle ABCD, then d = l + b .
A l B
Example 1: The perimeter of a rectangle is 28 m and its length is 8 m. Find its:
(a) breadth (b) area (c) diagonal

Solution: (a) Perimeter = 2(l + b)
⇒ 28 = 2(8 + b) ⇒ 28 = 16 + 2b ⇒ 2b = 12 ⇒ b = 6
∴ The breadth of the rectangle is 6 m.
(b) Area = l × b = 8 m × 6 m = 48 m 2

(c) Diagonal = l + 2 b = 2 8 + 2 6 m = 2 64 36 m = 100 m+ = 10 m

Example 2: Inside a rectangular field of dimension 24 m by 15 m, there is a path of uniform width 3 m.
Find the area of the path. 3 m

2
Solution: Area of the field including the path = 24 m × 15 m = 360 m 3 m 3 m
Length of the field excluding the path = 24 m – 3 m – 3 m 9 m 15 m
18 m
= 18 m 3 m
24 m

212