Question

If the area of an equilateral triangle is $81\sqrt{3}{\mathrm{cm}}^2$, find its height.

Answer 1

$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{equilateral}\mathrm{triangle}=\frac{\sqrt{3}}{4}\times (\mathrm{Side}{)}^2 \\ \Rightarrow \frac{\sqrt{3}}{4}\times (\mathrm{Side}{)}^2=81\sqrt{3} \end{gathered}$$
$$\begin{gathered} \Rightarrow (\mathrm{Side}{)}^2=324 \\ \Rightarrow \mathrm{Side}=18\mathrm{cm} \end{gathered}$$

Now, we have:
$$\begin{gathered} \mathrm{Height}=\frac{\sqrt{3}}{2}\times \mathrm{Side} \\ =\frac{\sqrt{3}}{2}\times 18 \\ =9\sqrt{3}\mathrm{cm} \end{gathered}$$