A Pentahedron over a Square Base

★ 5/10Law of Cosines solid geometry Triangle Geometry

Problem

As shown in the figure, in the pentahedron $ABCDEF$ the quadrilateral $ABCD$ is a square, the plane $ADE$ is perpendicular to the plane $ABCD$ , and $EF\parallel AB$ , with

AB=ED=2EF=2,\qquad \angle EAD=60^\circ.

Let $M$ be the midpoint of the edge $FC$ .

1. Prove that $AF\parallel$ plane $MBD$ .

2. Find the volume of the tetrahedron $E\text{-}FDB$ .

Answer

Solution

Difficulty	5/10
Topics	Law of Cosines, solid geometry, Triangle Geometry

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