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volume of tetrahedron related to area of projection of tetrahedron on plane

Source: 1997 ITAMO p4

January 25, 2020
geometry3D geometrytetrahedronprojection

Problem Statement

Let ABCDABCD be a tetrahedron. Let aa be the length of ABAB and let SS be the area of the projection of the tetrahedron onto a plane perpendicular to ABAB. Determine the volume of the tetrahedron in terms of aa and SS.
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