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 \(GHI\).
Submit your answers up to three decimal places.