2014 AIME II Problem 3

A rectangle has sides of length a and 36. A hinge is installed at each vertex of the rectangle and at the midpoint of each side of length 36 . The sides of length a can be pressed toward each other keeping those two sides parallel so the rectangle becomes a convex hexagon as shown. When the figure is a hexagon with the sides of length a parallel and separated by a distance of 24 , the hexagon has the same area as the original rectangle. Find a^{2}.