2012 AIME II Problem 5

In the accompanying figure, the outer square S has side length 40 . A second square S^{\prime} of side length 15 is constructed inside S with the same center as S and with sides parallel to those of S. From each midpoint of a side of S, segments are drawn to the two closest vertices of S^{\prime}. The result is a four-pointed starlike figure inscribed in S. The star figure is cut out and then folded to form a pyramid with base S^{\prime}. Find the volume of this pyramid.