In rectangle $ABCD$, points $F,G,H$ lie on $AB$ such that $AF=FG=GH=HB$. Point $E$ is the midpoint of $\overline{DC}$. Also, $\overline{AC}$ intersects $\overline{EF}$ at $P$ and $\overline{EG}$ at $Q$. The area of the rectangle $ABCD$ is $120$. Find the area of triangle $EPQ$.