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Pythagorean Pyramid (Posted on 2004-04-26) Difficulty: 3 of 5
The pictured tetrahedron has four identical rectangular (i.e., right-angled or pythagorean) triangles as faces, with

AB=CD=p,
AC=BD=q,
AD=BC=r,
and p+q=r.

What's its volume, as a function of p, q and r?






See The Solution Submitted by Federico Kereki    
Rating: 4.1250 (8 votes)

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Some Thoughts Slaying the Hedra (Spoiler) Comment 15 of 15 |

Given p^2 + q^2 = r^2, the Pythagorean equation for a right triangle in Euclidean geometry, it can be seen that the shape is NOT a three-dimensional tetrahedron but a two-dimensional tetragon with parallel sides of lengths p and q (thus a paralleogram) with polygon diagonals of length r.  Thus the shape has no volume but area only.
The AREA of the TETRAGON is then pq.


  Posted by Dej Mar on 2007-12-06 11:17:48
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