Question

The area of a regular hexagon of side 6 cm is __________.

Answer 1

Given: The side of a regular hexagon is 6 cm.

We know, a hexagon is formed by joining 6 equilateral triangles together.
Therefore,
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{hexagon}=\mathrm{Area}\mathrm{of}6\mathrm{equilateral}\mathrm{triangles} \\ =6\times \frac{\sqrt{3}}{4}\times x^2 \\ =6\times \frac{\sqrt{3}}{4}\times {\left(6\right)}^2 \\ =6\times \frac{\sqrt{3}}{4}\times 36 \\ =6\times 9\times \sqrt{3} \\ =54\sqrt{3}{\mathrm{cm}}^2 \end{gathered}$$

Hence, the area of a regular hexagon of side 6 cm is $\underline{54\sqrt{3}{\mathrm{cm}}^2}$.