This question has nearly no information and I've been stuck on this for quite some time. I tried drawing the median from A thru G but the 1x to 2x ratio didn't seem to help.
2026-03-28 20:55:58.1774731358
Ratio of area between similar triangles
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Hint: Draw the line $AG$, and suppose it meets $BC$ at the point $M$. Then by standard properties of the centroid, we have $AG=2GM$. This observation (which you made) is useful.
Note that the area of $\triangle DFE$ is the same as the area of $\triangle DME$, and that the area of $\triangle ADE$ is four-ninths of the area of $\triangle ABC$.