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

Let each side of an equilateral triangle be "a" cm
Area of an equilateral triangle $=81\sqrt{3}c{m}^2$ (Given)
Area of an equilateral triangle $=\frac{\sqrt{3}}{4}(side{)}^2$
$\Rightarrow 81\sqrt{3}=\frac{\sqrt{3}}{4}\times a^2$
$\Rightarrow a^2=324$
or $a=18cm$
Now,
Height of an equilateral triangle $=\frac{\sqrt{3}}{2}(side)=\frac{\sqrt{3}}{4}(18)=9\sqrt{3}cm.$
Perimeter $=3(side)=3\times 12=36cm$