The height of an equilateral triangle is $9\sqrt{3} $ cm . What is the area of this equilateral triangle ?

$ 81 \sqrt{3} cm^2$

Area of a equilateral triangle = \(\frac{\sqrt {3}}{4}\) × (side)²

The height of the equilateral triangle = \(\frac{\sqrt {3}}{2}\) × (side)

We have,

Height = $9\sqrt{3} $ 

$9\sqrt{3} $= \(\frac{\sqrt {3}}{2}\) × (side)

side = 18

Area of a equilateral triangle = \(\frac{\sqrt {3}}{4}\) × (18)²

= $ 81 \sqrt{3} cm^2$