2025 AMC 12A Problem 20

The base of the pentahedron shown below is a 13 \times 8 rectangle, and its lateral faces are two isosceles triangles with base of length 8 and congruent sides of length 13, and two isosceles trapezoids with bases of lengths 7 and 13 and nonparallel sides of length 13.

What is the volume of the pentahedron?

\textbf{(A)} 416 \qquad \textbf{(B)} 520 \qquad \textbf{(C)} 528 \qquad \textbf{(D)} 676 \qquad \textbf{(E)} 832

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.