What is the area of the equilateral triangle with the length of each side equal to a?

Area of equilateral triangle is whose side is given a = √3a^2/4

area of triangle 1/2*base * height

base = a

but height = √ a^2 - a^2/4

= √4a^2/4 - a^2/4.

=√3*a/2

now the formula is area of euqilateral traingle is 1/2*a*√3a/2

√3*a^2/4