Wednesday, September 30, 2015

Unizor - Geometry3D - Pyramids - Problem 2

Unizor - Creative Minds through Art of Mathematics - Math4Teens

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.

Pyramids - Problem 2

Given a triangular pyramid SABC with all side edges equal in length:
SA = SB = SC
All angles of the side faces at its apex S are right:
∠ASB = ∠BSC = ∠CSA = 90o.
The altitude from apex S onto base triangle ΔABC is SH=h.
Express in terms of altitude h all the edges, area of each face and volume of the pyramid.


Side edge: h√3
Base edge: h√6
Area of side face: 3h²/2
Area of base face: 3h²√3/2
Volume: h³√3/2

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