## 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.

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.

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