+470 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 $EF = 3$ and $HG = 10$, and the height of the trapezoid is $6$, then find the area of triangle $PFG$.
