# 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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