jmc

If you draw altitudes from $A$ and $B$ to $CD,$ the trapezoid will be divided into two right triangles and a rectangle. You can find the values of $a$ and $b$ with the Pythagorean theorem. $$a=\sqrt{15^2-12^2}=\sqrt{81}=9$$ $$b=\sqrt{20^2-12^2}=\sqrt{256}=16$$ $ABYX$ is a rectangle so $XY=AB=50.$ $$CD=a+XY+b=9+50+16=75$$ The area of the trapezoid is $$12\cdot \frac{(50+75)}{2}=6(125)=\boxed{750}$$