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