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 \(A'B'C'?\)
(第二十一届AIME2 2003 第6题)