Unizor - Geometry3D - Pyramids - Problem 5

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Notes to a video lecture on http://www.unizor.com

Pyramids - Problems 5

To effectively learn from problem solving, try to solve these problems just by yourself, then listen to a lecture and then try to solve them again by yourself.

Problem A

Given a regular tetrahedron SABC.
Draw a median AM within its triangular base ABC from vertex A to opposite side BC (M∈BC).
From its apex S draw a plane γ perpendicular to median of the base AM.
Assume that the area of a section of a pyramid formed by this plane equals to s.
Pick a midpoint P of median AM and construct another plane δ that is parallel to plane γ. It also cuts some section inside a pyramid.
What is the area of this section?

Answer:
9·s /16