Question

O is the centre of the circle. If AC = 28 cm, BC = 21 cm, ∠BOD = 90° and ∠BOC = 30°, then find the area of the shaded region given in the figure.

Answer 1

Given AC = 28 cm

BC = 21 cm

Since AB² = BC² + AC²

AB² = 28² + 21²

AB² = 784 + 441

AB = 35

Radius = `35/2`

Now area of shaded region = Area of circle − area of quadrilateral (AOD) − area of ΔABC

= `πr^2 − 1/4πr^2 − 1/2 xx BC xx AC`

= `3/4 xx 22/7 xx 35/2 xx 35/2 − 1/2 xx 28 xx 21`

= 427.875 cm²