Line through interior point intersects rectangle

Let rectangle $A B C D$ have lengths $A B = 20$ and $B C = 12$. Extend ray $B C$ to $Z$ such that $C Z = 18$. Let $E$ be the point in the interior of $A B C D$ such that the perpendicular distance from $E$ to $\overline{A B}$ is $6$ and the perpendicular distance from $E$ to $\overline{A D}$ is $6$. Let line $E Z$ intersect $A B$ at $X$ and $C D$ at $Y$. Find the area of quadrilateral $A X Y D$.