Question

If the area of an equilateral triangle is , find its height.

Answer 1

Area of the equilateral triangle = $81\sqrt{3}{\mathrm{cm}}^2$
Area of an equilateral triangle =$\left(\frac{\sqrt{3}}{4}\times a^2\right)$, where a is the length of the side.
$$\begin{gathered} \Rightarrow 81\sqrt{3}=\frac{\sqrt{3}}{4}\times a^2 \\ \Rightarrow 324=a^2 \\ \Rightarrow a=18\mathrm{cm} \end{gathered}$$
Height of triangle = $\frac{\sqrt{3}}{2}\times a$

$$\begin{gathered} =\frac{\sqrt{3}}{2}\times 18 \\ =9\sqrt{3}\text{cm} \end{gathered}$$