If the height of an equilateral triangle is 20\(\sqrt {3 }\) cm. Then the area is- 

400\(\sqrt {3}\) cm²

Heigth = \(\frac{\sqrt {3}}{2}\) x a = 20\(\sqrt {3}\)

a = 40

Area = \(\frac{\sqrt {3}}{4}\) x a² = \(\frac{\sqrt {3}}{4}\) x 40² = 400\(\sqrt {3}\) cm²

Alternate:

In a equilateral triangle:

if Side = 2a, then

Heigth = \(\frac{\sqrt {3}}{2}\) x 2a

Area = \(\frac{\sqrt {3}}{4}\) x 4a²

Relation in ratio to be remember for equilateral triangle:

Side    :    Height    :    Area

2a    :    \(\frac{\sqrt {3}}{2}\) x 2a    :    \(\frac{\sqrt {3}}{4}\) x 4a²

2a    :    \(\sqrt {3}\) a    :    \(\sqrt {3}\) a²

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Now according to question:

Height = \(\sqrt {3}\) a = 20\(\sqrt {3}\)

a = 20

Area = \(\sqrt {3}\) a² =  400\(\sqrt {3}\) cm²