If the height of an equilateral triangle is $20\sqrt{2}$ cm, then what is its area (in cm²)?

$\frac{800}{3}\sqrt{3}$

We know that,

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

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

We have,

the height of an equilateral triangle is $20\sqrt{2}$ cm

\(\frac{\sqrt {3}}{2}\) × (side) = $20\sqrt{2}$ 

side = \(\frac{40\sqrt{2}}{\sqrt {3}}\)

So, Area of a equilateral triangle = \(\frac{\sqrt {3}}{4}\) × (\(\frac{40\sqrt{2}}{\sqrt {3}}\))²

= $\frac{800}{3}\sqrt{3}$