Question

A regular hexagon is inscribed in a circle. If the area of hexagon is $24\sqrt{3}c{m}^2$, find the area of the circle. (Use $\pi$ $=3.14$).

Answer 1

$\Rightarrow$ Let the radius of the circle be $r$ and side of hexagon be $a$.

$\Rightarrow$ Area of hexagon $=\frac{3\sqrt{3}}{2}{a}^2$

$\Rightarrow$ $24\sqrt{3}=\frac{3\sqrt{3}}{2}{a}^2$

$\Rightarrow$ $a^2=16$

$\therefore$ $a=4cm$

In an regular hexagon inscribed in a circle, its side is equal the radius.

$\therefore$ $r=a=4cm$

$\Rightarrow$ Area of circle $=\pi r^2=3.14\times (4{)}^2$

$\therefore$ Area of circle $=50.24c{m}^2$