Draw the line parallel to $\overline{A}$ D}$through$E$, intersecting \overline{A B}$ at $F$ and $\overline{C}$ D}$at$G$. It is clear that$X F E$and$Y G E are congruent, so the area of A X Y D$is equal to that of$A F G D$. But$A F G D is simply a 12 by 6 rectangle, so the answer must be 72 . (Note: It is also possible to directly compute the values of A X$and$D Y$, then use the formula for the area of a trapezoid.)