I want to derive the formula for the area of an equilateral triangle by integrating a simple formula for its perimeter. Here's my attempt that doesn't work.
I want to know why it doesn't work.
3 * side = perimeter
area = integral of perimeter wrt side
area = 3/2 * side^2
But I know that the real formula is area = (sqrt(3)/4) * s^2.
So what's wrong with the way I'm trying to get the formula?
Cheers