Seems difficult at first glance, but is it?
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 \(A'B'C'\)?
This is in the set Contest Problems
This is an AIME Problem