Geometry_4

Solution:


The image above should explain things pretty well but here’s a summary:

I first found the ratios of lengths involving E_n using Menelaus’s Theorem.
Then I found ratios of lengths involving D_n using Mass Points (could use Menelaus again)

Note that G is the centroid for D_1D_2D_3, E_1E_2E_3, and A_1A_2A_3 as we can just set the latter to be an equilateral triangle (because the ratios of areas will hold for any triangle).

From here we can just compare the lengths of the median of each respective triangle and square them to get the ratio of their areas.
\frac{25}{49} is my final answer.

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