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So, we can say that the area of the circle = Area of the parallelogram = base × height

1
= (2pr) × r = pr 2
2
2
So, the area of a circle = pr sq. units
Similarly, if we divide the circle in 64 sectors, and arrange these sectors, it gives nearly a rectangle
of length of the half of circumference of circle and breadth is equal to the radius.

1 circumference Radius
2
Thus, the area of the circle = Area of the rectangle = length × breadth
1
= ( 2πr) ×= πr 2
r
2
2
In both cases, it is clear that the area of the circle = pr Maths Talk
 22  If a circle, a rectangle, a
Example 22: Find the area of a circle of radius 21 cm. Take π= 7   triangle and a square have


one has the greatest area?
Solution: We have, area of a circle = pr = 22 × 21 cm × 21 cm the same perimeter, which
2
7
= 1386 cm 2
Thus, the area of the circle is 1386 cm 2
 22 
Example 23: If the circumference of a circle is 44 m, find its area. Take π= 7 



Solution: Let radius of the circle be r.
We have, circumference of a circle = 2pr = 44 m

\ 2 × 22 × r = 44 m Quick Check
7 1. The radius of a circle is 4 inches.
×
\ r = 744 m = 7 m
×
222 What is the area of the circle? 2
Therefore, the radius of the circle is 7 m. 2. If the area of a circle is 154 cm ,
what is the radius of the circle?

2
Now, the area of the circle = pr = 22 × (7 m) 2 3. A dinner plate’s radius is 8 cm.
7 What is the area of the plate?
22
2
2
= × 49 m = 22 × 7 m = 154 m 2
7
2
Thus, the area of the circle is 154 m .
Area between two Concentric Circles A
R
Circles with the same centre but different radii are called ‘concentric circles’ O B
From the figure, it is clear that: r

Area between circles (the shaded region) = area of outer circle – area of inner circle
2
2
= pR – pr = p(R – r )
2
2
297 Perimeter and Area