Question:
If the area of an equilateral triangle is $81 \sqrt{3} \mathrm{~cm}^{2}$, find its height.
Solution:
Area of equilateral triangle $=\frac{\sqrt{3}}{4} \times(\text { Side })^{2}$
$\Rightarrow \frac{\sqrt{3}}{4} \times(\text { Side })^{2}=81 \sqrt{3}$
$\Rightarrow$ (Side) $^{2}=324$
$\Rightarrow$ Side $=18 \mathrm{~cm}$
Now, we have:
Height $=\frac{\sqrt{3}}{2} \times$ Side
$=\frac{\sqrt{3}}{2} \times 18$
$=9 \sqrt{3} \mathrm{~cm}$