show that the area of an equilateral triangle is r00t3/4 x^2 where x is side of triangle.

side is x
thus using herons formula area = sqrt( s(s-a)(s-b)(s-c) ) where a=b=c= x and s = (a+b+c)/2 = 3x/2
thus area = sqrt( s(s-a)(s-b)(s-c) )
=sqrt((3x/2)( 3x/2 -x ) ( 3x/2 -x )( 3x/2 -x ) )
= sqrt( (3x/2)(x/2)(x/2)(x/2) )
=  sqrt( (3/16)(x^4) )
= sqrt(3) * x^2/4