AMC 12A 2025 (Problem 20)

The base of the pentahedron shown below is a

13\times8

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?

\text{(A)}\;416

\text{(B)}\;520

\text{(C)}\;528

\text{(D)}\;676

\text{(E)}\;832