A fuel storage tank is in the shape of an equilateral triangular prism. The prism is 8 feet high and 10 feet long. When the tank is half-full, the depth of the fuel is what?

Question

note: I know the only way to find the depth is to cut the triangle in half horizontally creating another triangle and a trapezoid and make the height of the trapezoid the depth of the half full tank (variable h) but how do i find that?/?

Answer 1

think about similar triangles.
1/2 the altitude means 1/4 the area
or, conversely, 1/2 the area means 1/√2 the altitude