# Problem of the Week Problem E Across the Prism

A trapezoidal prism is a prism in which opposite parallel ends are congruent trapezoids.

For the trapezoidal prism shown, the opposite parallel sides of each trapezoid are $$36$$ cm and $$16$$ cm in length. The non-parallel sides of each trapezoid are $$16$$ cm and $$12$$ cm in length. The prism is $$40$$ cm long. The volume of the prism is $$9984$$ cm$$^3$$.

A body diagonal of a prism is a line connecting two vertices that are not on the same face. Find the length of the body diagonal $$AB$$ (indicated in the diagram), accurate to $$1$$ decimal place.