Page 234 - ICSE Math 7

21 Perimeter and Area

Key Concepts

• Perimeter and Area of a Rectangle and a Square • Circumference and Area of a Circle
• Area of a Triangle and a Parallelogram

One should remember that Mathematics is not a spectator sport. It is a valuable tool that can be used
in everyday life, and the more it is applied the more useful it becomes.

Suppose a teacher allocates two projects to all the students of a class: to find the length of the border
to be put around the bulletin board and to find how much carpet is needed for the floor of the music
room of the school. Do you know what is to be determined in the above two projects? Is it perimeter
in the first project and area in the second project?

In the previous class, we have studied about perimeters and areas of some plane figures including
squares and rectangles. In this chapter, we will learn about perimeter and area of some more plane
figures such as triangles and parallelograms. We will also learn how to find circumference and area
of a circle.

Squares and Rectangles

Let’s review some definitions and formulas learnt earlier. b
Perimeter is the length of the boundary of a closed plane figure.

Perimeter of a rectangle = 2 × (length + breadth) = 2 × (l + b) l
Perimeter of a square = 4 (side) = 4 × a

Area is the surface or region enclosed inside a closed boundary. a
Area of a rectangle = length × breadth = l × b
a
Area of a square = side × side = a × a

Conversion of units

The area of a region formed by a square of Length Area
2
side 1 cm is called a square centimetre and 1 cm = 10 mm 1 cm = 100 mm 2
2
written as 1 cm . The area of a square of 1 dm = 10 cm 1 dm = 100 cm 2
2
side 1 decametre (1 dam) is called an are and 2 2
2
written as 1 dam or 1 are. The area of a region 1 m = 10 dm 1 m = 100 dm
2
formed by a square of side 1 hectometre 1 dam = 10 m 1 m = 10,000 cm 2
2
(1 hm) is called a hectare, written as 1 hm . 1 hm = 10 dam 1 km = 10,00,000 m 2
2
It is also possible to convert length and area 2
from one unit to the other. 1 km = 10 hm 1 are = 100 m
1 m = 100 cm 1 hectare = 10,000 m 2
1 km = 1,000 m 1 hectare = 100 are

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