jmc

We add the edges of the pyramid to our diagram below.



Taking $ABC$ to be the base of pyramid $ABCH$, the height is $HD$. Therefore, the volume of pyramid $ABCH$ is $$\frac{[ABC](HD)}{3}.$$We are given that this volume equals 20, so we have $$[ABC]\cdot HD=60.$$The volume of prism $ABCDEFGH$ is the product of area of $ABCD$ and the height of the prism, which equals $HD$. The area of $ABC$ is half the area of rectangle $ABCD$, so we have $$\begin{array}{rl}\text{Volume of }ABCDEFGH& =([ABCD])(HD)\\ & =2([ABC])(HD)\\ & =\boxed{120}.\end{array}$$