AMC 8 2018 Problem 22

Point $E$ is the midpoint of side $\overline{CD}$ in square $ABCD,$ and $\overline{BE}$ meets diagonal $\overline{AC}$ at $F.$ The area of quadrilateral $AFED$ is $45.$ What is the area of $ABCD?$

$\textbf{(A) } 100 \textbf{(B) } 108 \textbf{(C) } 120 \textbf{(D) } 135 \textbf{(E) } 144$