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Question
In the given figure ABCD is a rectangle. It consists of a circle and two semi-circles each of
which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to
three significant figures
Solution
Length of a rectangle = Radius of two semi-circles Diameter of a circle
= 5 + 5 + 10
= 20 cm
Breadth of a rectangle = Diameter of a circle = 2 x 5 = 10 cm
∴ Area of a rectangle = Length x Breadth
= 20 x 10
= 200 sq. cm
Area of circle = `22/7 xx 5 xx 5` = 78.571 sq.cm
And, area of two semi-circles each of radius 5 cm = `2(1/2 xx 78.571)` = 78.571 sq. cm
Now,
Area of shaded region = Area of a rectangle - Area of a circle - Area of two semi- circle
= 200 - 78.571 - 78.571
= 200 - 157.142
= 42.858 sq.cm
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