Question 24
Let $ABCD$ be a parallelogram of area $10$ with $AB=3$ and $BC=5.$ Locate $E,$ $F,$ and $G$ on segments $\overline{AB},$ $\overline{BC},$ and $\overline{AD},$ respectively, with $AE=BF=AG=2.$ Let the line through $G$ parallel to $\overline{EF}$ intersect $\overline{CD}$ at $H.$ The area of the quadrilateral $EFHG$ is