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)