Question

In the given figure, three sectors of a circle of radius 7 cm, making angles of ${60}^{\circ },{80}^{\circ }and{40}^{\circ }$ at the centre are shaded. Find the area of the shaded region.

Answer 1

Area of the shaded region = Area of the sector having central angle ${60}^o$ + Area of sector having central angle ${80}^o$ + Area of the sector having central angle ${40}^o$

$=[\frac{{60}^o}{{360}^o}\times \pi (7{)}^2]+[\frac{{80}^o}{{360}^o}\times \pi \left(7{)}^2\right]+[\frac{{40}^o}{{360}^o}\times \pi (7{)}^2]=\pi (7{)}^2(\frac{{60}^o}{{360}^o}+\frac{{80}^o}{{360}^o}+\frac{{40}^o}{{360}^o})=\pi \left(7{)}^2\right(\frac{{180}^o}{{360}^o})=\frac{22}{7}\times (7{)}^2\left(\frac{1}{2}\right)=77c{m}^2$

Hence, the area of the shaded region is $77c{m}^2$.