2003 AIME II Problem 6

In \triangle A B C, A B=13, B C=14, A C=15, and point G is the intersection of the medians. Points A^{\prime}, B^{\prime}, and C^{\prime} 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 A B C and A^{\prime} B^{\prime} C^{\prime} ?