# Napoleon's?

Geometry Level 5

Define triangle $$ABC$$ with $$AB=55$$ units, $$BC=60$$ units and $$AC=49$$ units. Let $$D, E$$ and $$F$$ be points outside the triangle such that triangles $$ABD$$, $$BCE$$ and $$ACF$$ are equilateral. Points $$G, H$$ and $$I$$ are the centroids of the three equilateral triangles, respectively. Find the area of triangle $$GHI$$.