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In trapezoid $EFGH,$ $\overline{EF} \parallel \overline{GH},$ and $P$ is the point on $\overline{EH}$ such that $EP:PH = 2:5$.  If the area of triangle $PEF$ is $4$, and the area of triangle $PGH$ is $8$, then find the area of trapezoid $EFGH$.

 
 Dec 14, 2023

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