2003 AIME II Problem 6

In triangle ABC, AB = 13, BC = 14, AC = 15, and point G is the intersection of the medians. Points A', B', and C', are the images of A, B, and C, respectively, after a 180^\circ rotation about G. What is the area of the union of the two regions enclosed by the triangles ABC and A'B'C'?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.