Question

show that the area of an equilateral triangle is
$\frac{ \sqrt{3} }{4} {x}^{2}$
where x is side of the triangle.

Answer 1

using herons formula
we have: s=1/2(X+X+X)=3x/2
so, (s_x)=[3x/2_x]=X/2, (s_b) =(3x/2_x). =X/2
and. (s_c). = (3x/2_x)
by herons formula we have
area =√s(s_a) (s_b) (s_c)sq unit
√3x/2×x/2×x/2×x/2 sq unit
= [√3xsquare/4]
this is your answer