Question

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

Answer 1

Given that
we know that $Area=\frac{\sqrt{3}}{4}\times a^2$
area of the equilateral triangle = 81$\sqrt{3}c{m}^2$

$\frac{\sqrt{3}}{4}\times a^2=81\sqrt{3}$
$\frac{1}{4}{a}^2=81$
$a^2=81\left(4\right)$
$a^2=324$
a = 18cm

Then the height of the equilateral triangle $=\frac{\sqrt{3}a}{2}$
$=\frac{\sqrt{3}}{2}\times 18=9\sqrt{3}cm$