Question

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

 

Answer 1

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`