Question

ABCDEF is a regular hexagon with center O. If the area of triangle $9c{m}^2$, find the area of (i) the hexagon and (ii) the circle in which the hexagon inscribed.

Answer 1

Area of $△AOB=\frac{9}{2}$

Let the side of hexagon be $a$

$\frac{\sqrt{3}}{4}{a}^2=\frac{9}{2}{a}^2=18\sqrt{3}a=\sqrt{9\times 2\times \sqrt{3}}a=3.2^{\frac{1}{2}}.3^{\frac{1}{4}}$

Area of Hexagon$=6\times$ area of $△AOB$

$=6\times \frac{9}{2}=27$

Area of circle$=\pi r^2$

the circle radius$r=a$

Area$=\pi a^2=\pi \times 9\times 2.\sqrt{3}=18\pi \sqrt{3}$