So for example if we have trapezoid ABCD then we could draw diagonal BD and AC. They would intersect at a point and create four triangles. So say that we knew the area of the two triangles whose bases are the parallel sides of the trapezoid. Let's call the areas A and B. The area of the trapezoid would then be A+B+2sqrt(AB). My question is how would you derive this formula?
Right now, I'm thinking of using the fact that the two triangles A and B are similar to each other and so their heights and bases would be similar. So we know their heights are similar and the triangles' heights also add up to the height of the trapezoid. That's my lead, but I'm not sure if that will go anywhere.
Anyone know how to derive the formula?