Question

A regular hexagon is inscribed in a circle of radius 14 cm as shown in fig. 6.31. Find the area of shaded portion. [$\mathrm{\pi }=\frac{22}{7},\sqrt{3}=1.73]$

Answer 1

Radius (r) of circle = 14 cm
Side of regular hexagon = radius of circle = 14 cm

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{circle}=\pi r^2 \\ =\frac{22}{7}\times 14\times 14 \\ =616{\mathrm{cm}}^2 \end{gathered}$$

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{regular}\mathrm{hexagon}=\frac{3\sqrt{3}}{2}(\mathrm{side}{)}^2 \\ =\frac{3\times 1.73}{2}(14{)}^2 \\ =508.62{\mathrm{cm}}^2 \end{gathered}$$

$\therefore$ Area of the shaded portion = area of circle − area of hexagon
= (616 – 508.62) cm²
= 107.38 cm²