in this figure as shown,let the side be "s",height =s√3/2
area of the right angled triangle= 1/2(half) X base x height .
therefore since there are 2 right angled triangles the area is 1/2 x s/2 x s√3/2+1/2 x s/2 x s√3/2. therefore area = 1/2 x s ( S√3/2)=1/2 x square of s x √3/2 = square of s x √3/4.
hence proved that area of an equilateraltriangle = SQUARES of s X √3/4.
Perimeter
perimeter of an equilateral triangle = sum of all 3 sides .