Question

How to express the area of an equilateral triangle in terms of its side?

Answer 1

Let  the side be x  and the altitude be a
a^2 = x^2 - (0.5x)^2
a^2 = 0.75x^2

a = sqrt0.75 x

so the area = 0.5x * a  = 0.5x * sqrt0.75 x^2 = 0.433x^2