Monday, October 5, 2015
Unizor - Geometry3D - Pyramids - Problems 4
Unizor - Creative Minds through Art of Mathematics - Math4Teens
Notes to a video lecture on http://www.unizor.com
Pyramids - Problems 4
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.
Given a right rectangular prism ABCDA'B'C'D' with three edges with common vertex A having length x, y and z.
Let's connect with straight lines vertices
A and C,
A and B',
A and D',
C and B',
C and D',
B' and D'.
What is the volume of tetrahedron ACB'D' formed by these vertices?
Given a triangular pyramid SABC with pairs of opposite edges equal to each other as follows:
SA = BC = a,
SB = AC = b,
SC = AB = c.
What is the volume of this pyramid?
where m = (a²+b²+c²) /2
Use the Problem A above.