Question

Find the sum of the areas of the shaded sectors given that ABCDEF is any hexagon and all the circles are of same radius r with different vertices of the hexagon as their centres as shown in the figure.

• 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 B

$2\pi r^2$

Sum of interior angles of a hexagon = ${720}^{\circ }$
6 sectors with same radius r = 2$\times$(full circles of same radius).
So area of shaded region $\Rightarrow 2\pi r^2$