I need the equation for finding the height of a trapezoid!

That equation is complicated. The four sides of the trapezoid are a, b, c and d.

height² = [ (a + b - c + d) • (-a + b + c + d) • (a - b - c + d) • (a + b - c - d) ] : (4 • (a - c) ²)

If you know the trapezoid area then you calculate:

height = (2 * trapezoid area) / (sum of the parallel sides)