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.