Question

A regular hexagon is inscribed in a circle of radius 6 cm. Find the area of shaded portion.
$(\sqrt{3}=1.73,\mathrm{\pi }=3.14)$ (Fig. 9.27)

Answer 1

Radius (r) of the circle = 6 cm
We know that the diagonals of a regular hexagon divide it into six equilateral triangles.
i.e., side of the regular hexagon = radius of the circle = 6 cm
Area of the circle =$\pi r^2$
= 3.14× (6 cm)²
= 113.04 cm²

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{regular}\mathrm{hexagon}=\frac{3\sqrt{3}}{2}(\mathrm{side}{)}^2 \\ =\frac{3\sqrt{3}}{2}(6\mathrm{cm}{)}^2 \\ =\frac{3\times 1.73\times 36}{2}{\mathrm{cm}}^2 \\ =93.42{\mathrm{cm}}^2 \end{gathered}$$


∴ Area of the shaded portion = area of the circle − area of the regular hexagon
= (113.04 – 93.42) cm_²
= 19.62 cm²