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Rotation about a Centroid

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December 26, 2006
geometrygeometric transformationrotationratioAMCAIME

Problem Statement

In triangle ABC,ABC, AB=13,AB=13, BC=14,BC=14, AC=15,AC=15, and point GG is the intersection of the medians. Points A′,A', B′,B', and C′,C', are the images of A,A, B,B, and C,C, respectively, after a 180∘180^\circ rotation about G.G. What is the area if the union of the two regions enclosed by the triangles ABCABC and A′B′C′?A'B'C'?
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