Question 9In the figure, $ABCD$ is a $2$ by $2$ square, $E$ is the midpoint of $\overline{AD},$ and $F$ is on $\overline{BE}.$ If $\overline{CF}$ is perpendicular to $\overline{BE},$ then the area of quadrilateral $CDEF$ is $2$$3-\frac{\sqrt3}{2}$$\frac{11}{5}$$\sqrt5$$\frac94$
