Question 16In rectangle $ABCD,$ $AB=1,$ $BC=2,$ and points $E,$ $F,$ and $G$ are midpoints of $\overline{BC},$ $\overline{CD},$ and $\overline{AD},$ respectively. Point $H$ is the midpoint of $\overline{GE}.$ What is the area of the shaded region? $\dfrac1{12}$$\dfrac{\sqrt3}{18}$$\dfrac{\sqrt2}{12}$$\dfrac{\sqrt3}{12}$$\dfrac16$
