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Find the area of an equilateral triangle having altitude *h* cm.

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#### Solution

Altitude of a equilateral triangle, having side *a *is given by

Altitude = `sqrt(3)/2 a`

Substituting the given value of altitude *h *cm, we get

`h = sqrt(3)/2 a`

`a = 2/sqrt( 3) h cm `

Area of a equilateral triangle, say *A* having each side *a* cm is given by

`A= sqrt(3)/4 a^2`

Area of the given equilateral triangle having each equal side equal to `2/sqrt(3) h cm ` is given by;* *

`A = sqrt(3)/4 ( 2/sqrt(3) h cm )^2`

`A = sqrt(3)/4 xx 4/3 h^2`

`A = h^2/sqrt(3)cm ^2`

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