Question

In the given figure, AB is the diameter of a circle with center O and OA = 7 cm. Find the area of the shaded region.

Answer 1

Given, OA = 7 cm.

Area of small circle = πr²

Where, r = `7/2`

∴ Area of circle = `22/7 xx 7/2 xx 7/2`

= `77/2`

= 38.5 sq. cm.

Area of two shaded segments = Area of big semicircle – Area of ΔCBD

= `1/2 π xx 7^2 - 1/2 xx 7 xx 14`

= `1/2 xx 22/7 xx 49 - 7 xx 7`

= 11 × 7 – 7 × 7

= 77 – 49

= 28 sq. cm.

∴ Total shaded area

= 38.5 + 28 

= 66.5 sq. cm.