Question

find the area of equilateral triangle with measure of side area a,b, c by using multiple double integration

Answer 1

if it is equilateral why does it have three different side lengths?

Answer 2

Assume the base is along the x axis.
Assuming the vertex is between the ends of the base and has x-coordinate v, then if the two sides have equations

y = mx+n and y = hx+k, then just integrate

∫[0,v]∫[0,mx+n] dy dx + ∫[v,a]∫[0,hx+k] dy dx

If v is not directly over the base, things get more complicated...