The height of an equilateral triangle is 6 cm. Its area is

Explanation

Let each side of the given triangle be a cm.
Then, its height `=((sqrt(3))/(2)xxa)cm`.
`therefore" "(sqrt(3))/(2)xx "a cm"= "6 cm" rArr a = ((6 xx 2)/(sqrt(3)))`
`rArr" ""side"=4 sqrt(3)` cm.
`therefore" "`area of the given triangle
`=((sqrt(3))/(4)xx a^(2))"sq units"={(sqrt(3))/(4) xx (4 sqrt(3))^(2)}cm^(2)`
`=((sqrt(3))/(4)xx 48)cm^(2)=12 sqrt(3) cm^(2)`.
Hence, the area of the given triangle is `12 sqrt(3) cm^(2)`.