>>13450739Menelaus's theorem twice gives pic related ratios. Symmetry assumptions do not alter the ratios between the areas. Assuming maximum symmetry both the outer and inner triangles would be equilateral. The side of the inner triangle would be equal to sqrt((sqrt(3)/2)^2 + (1/6)^2) * (5/12) times the side of the outer triangles, giving the ratio of the areas to be: (28/36) * (25 / 144) = 175/1296
That is, the outer triangle has an area of
1296 / 175 = 7.40571... times the area of the inner triangle.
