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volume of pentahedron (2017 Adygea Teachers' Geometry Olympiad p4 RU)

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June 21, 2020
geometry3D geometrytetrahedronVolume

Problem Statement

A regular tetrahedron SABCSABC of volume VV is given. The midpoints DD and EE are taken on SASA and SBSB respectively and the point FF is taken on the edge SCSC such that SF:FC=1:3SF: FC = 1: 3. Find the volume of the pentahedron FDEABCFDEABC.
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