+1678 In trapezoid $EFGH,$ $\overline{EF} \parallel \overline{GH},$ and $P$ is the point on $\overline{EH}$ such that $EP:PH = 1:2$. If the area of triangle $PEF$ is $4$, and the area of triangle $PGH$ is $4$, then find the area of trapezoid $EFGH$.
