jmc

Since $\overline{PA}$ is perpendicular to both $\overline{AB}$ and $\overline{AD}$, the segment $\overline{PA}$ is the altitude from the apex to the base of the pyramid. To find this length, consider right triangle $PAB$. Applying the Pythagorean Theorem gives $PA=\sqrt{P{B}^2-A{B}^2}=15$.

The area of the base is $[ABCD]=(AB)(BC)=32$, so the volume of the pyramid is $\frac{1}{3}(32)(15)=\boxed{160}$ cubic units.