Seems difficult at first glance, but is it?

Geometry Level 4

In \(\triangle ABC\), \(AB=13\), \(BC=14\), and \(AC=15\). Point \(G\) is the intersection of the medians of \(\triangle ABC\). Points \(A',B',\) and \(C'\) are the images of points \(A,B,\) 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 \(A'B'C'\)?

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