Question

ABCDEF is a regular hexagon with centre O. If area of triangle OAB is $9c{m}^2$, find the area of the circle in which the hexagon is inscribed.

Answer 1

Given: Area of $△OAB=9c{m}^2$

We know that a regular hexagon is made up of $6$ equilateral triangles.

But area of each equilateral triangle $=9$

$\Rightarrow$ $\frac{\sqrt{3}}{4}\times (side{)}^2=9$

$\Rightarrow$ $(side{)}^2=\frac{36}{\sqrt{3}}$

For the circle in which the hexagon is inscribed, its radius $r=$ side of the hexagon

Now, Area of a circle $=\pi r^2$

$\Rightarrow$ Area of a circle $=\frac{22}{7}\times \frac{36}{\sqrt{3}}$

$\therefore$ Area of a circle $=65.32c{m}^2$