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

Answer 1

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