Question

In Fig. $PQR$ is an equilateral triangle. Arcs have been drawn with radii $14cm$ each and with centres $P,Q$ and $R$. The area of the shaded region is

• A. $102.6$ $c{m}^2$
• B. $206$ $c{m}^2$
• C. $308$ $c{m}^2$
• D. $345$ $c{m}^2$

Answer 1

The correct option is C $308$ $c{m}^2$

Radius of each circle $=14cm$

Angle subtended by each arc at centre $={60}^0$

Area of shaded region $=3\times$ Area of one sector with radius $14cm$ and angle ${60}^0$

$=3\times \frac{60}{360}\pi {14}^2{cm}^2$

$=\frac{22}{7}\times {14}^2{cm}^2$

$=308{cm}^2$