Question

Find the area of a regular hexagon having side $a$.

Answer 1

Find the area of the hexagon

We know that a hexagon has $6$ equilateral triangles

Given that each side of the hexagon is $a$

Therefore, each side of the equilateral triangle is $a$

The area of an equilateral triangle $\mathbf{=}\frac{\sqrt{\mathbf{3}}}{\mathbf{4}}\mathbf{·}{\mathit{a}}^{\mathbf{2}}$

$$\begin{gathered} \therefore \mathrm{Area}\mathrm{of}\mathrm{Hexagon}=6·\frac{\sqrt{3}}{4}.{\mathrm{a}}^2 \\ =\frac{3\sqrt{3}}{2}{\mathrm{a}}^2 \end{gathered}$$

Hence, the area of the hexagon with each side $a$ is $\frac{3\sqrt{3}}{2}{\mathrm{a}}^2$