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imc

geometry intermediate

Problem

In the rectangular parallelepiped shown, = , = , and = . Point is the midpoint of . What is the volume of the rectangular pyramid with base and apex ?
problem
(A)
(B)
(C)
(D)
(E)
Solution
Consider the cross-sectional plane and label its area . Note that the volume of the triangular prism that encloses the pyramid is , and we want the rectangular pyramid that shares the base and height with the triangular prism. The volume of the pyramid is , so the answer is .(AOPS12142015)
Final answer
E