Question

$ABCDE$ is any pentagon. In the given figure all the circles have their centres at the vertices and are all of equal radius $r$. The area of all the shaded sectors is

• A. $\pi r^2$
• B. $2\pi r^2$
• C. $\frac{5\pi r^2}{4}$
• D. $\frac{3\pi r^2}{2}$

Answer 1

The correct option is D $\frac{3\pi r^2}{2}$

Sum of all the central angles of the circles which are shaded $=$ Sum of all the interior anglesof the pentagon $=6$ right angles
Central angle of one full circle $=4$ right angles.
and area of one circle $=\pi r^2$
$\therefore$ Area of the shaded sectors $=\frac{6\times \pi r^2}{4}=\frac{3\pi r^2}{2}$