The area of an equilateral triangle is $9\sqrt{3}\text{sq cm}$. Find the height of the triangle.

Let the side of the equilateral triangle be $a$.The formula for the area of an equilateral triangle is:
$$\text{Area}=\frac{\sqrt{3}}{4}{a}^2$$
Given:
$$\frac{\sqrt{3}}{4}{a}^2=9\sqrt{3}$$
$$a^2=36⟹a=6\text{cm}$$
The height ($h$) of an equilateral triangle is given by the formula:
$$h=\frac{\sqrt{3}}{2}a$$
$$h=\frac{\sqrt{3}}{2}\times 6=3\sqrt{3}\text{cm}$$