Unizor - Geometry3D - Pyramids - Problems 4

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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.

Problem A

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?

Answer:
x·y·z /3

Problem B

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?

Answer:
√[(m−a²)·(m−b²)·(m−c²)] /3
where m = (a²+b²+c²) /2

Hint:
Use the Problem A above.