jmc

In order to find the area of trapezoid $WXYZ$, we must find the lengths of both bases and the distance (height) between those bases.



We add $\overline{WY}$ to our diagram and note that because $\overline{WX}\parallel \overline{ZY}$ and $\overline{WY}\perp \overline{ZY}$, we have $\overline{WY}\perp \overline{WX}$. Therefore, triangles $WYX$ and $WYZ$ are right triangles.

From right triangle $WYZ$, we have $\tan Z=\frac{WY}{ZY}$, so $WY=ZY\cdot \tan Z=12\cdot 1.5=18$. From right triangle $WXY$, we have $\tan X=\frac{WY}{WX}$, so $$WX=\frac{WY}{\tan X}=\frac{18}{3}=6.$$Therefore, the area of $WXYZ$ is $$\frac{WX+YZ}{2}\cdot WY=9\cdot 18=\boxed{162}.$$