Question

A regular hexagon is inscribed in a circle. If the area of hexagon is \[24\sqrt{3}\] , 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 =\[\frac{3\sqrt{3}}{2} a^2\]

\[\Rightarrow 24\sqrt{3} = \frac{3\sqrt{3}}{2} a^2 \]
\[ \Rightarrow a^2 = 16\]
\[ \Rightarrow a = 4 cm\]

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 

\[\pi r^2 \]
\[ = 3 . 14 \times 4 \times 4\]
\[ = 50 . 24 {cm}^2\]