Question

A regular hexagon is inscribed in a circle of radius $6$ cm. Find its area (in cm${}^2$).

• A. $48\sqrt{3}$
• B. $54\sqrt{3}$
• C. $48\sqrt{2}$
• D. $54\sqrt{2}$

Answer 1

The correct option is B $54\sqrt{3}$

When a regular hexagon is inscribed in a circle of radius , $a$, its length of side will also be $a$
Area of the hexagon of side "a" $=\frac{3\sqrt{3}}{2}{a}^2$
So, area of hexagon of side $6cm$ is $=\frac{3\sqrt{3}}{2}{\left(6\right)}^2=54\sqrt{3}$ sq cm