Question 9
Let $ABCD$ be a rectangle with $AB \gt BC$, and $O$ be the point of intersection of its diagonals $AC$ and $BD$. Angle bisector $B\hat{A}C$ cuts $BD$ at $E$. We call $M$ the midpoint of $AB$. The perpendicular to $AB$ is drawn through $E$, which cuts $AB$ at $F$; The perpendicular to $AE$ is drawn through $E$, which cuts $AC$ at $H$. If $OH = a$ and $MF = \frac{4}{3}a$ are given, calculate the area of rectangle $ABCD$ in terms of $a$.