Question

A regular hexagon is inscribed in a circle. If the area of hexagon is $24\sqrt{3}$ cm², find the area of the circle. (Use π = 3.14)

Answer 1

Let the radius of the circle be r and side of hexagon be a.
Area of hexagon = $\frac{3\sqrt{3}}{2}{a}^2$
$$\begin{gathered} \Rightarrow 24\sqrt{3}=\frac{3\sqrt{3}}{2}{a}^2 \\ \Rightarrow a^2=16 \\ \Rightarrow a=4\mathrm{cm} \end{gathered}$$
In an regular hexagon inscribed in a circle, its side is equal the radius.
∴ r = a = 4 cm
Now, Area of circle is given by
$$\begin{gathered} {\mathrm{\pi r}}^2 \\ =3.14\times 4\times 4 \\ =50.24{\mathrm{cm}}^2 \end{gathered}$$