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 length $7$ and $13$ and nonparallel sides of length $13$. What is the volume of the pentahedron? $\textbf{(A)}~416\qquad$ $\textbf{(B)}~520\qquad$ $\textbf{(C)}~528\qquad$ $\textbf{(D)}~676\qquad$ $\textbf{(E)}~832$