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Volume of a tetrahedron?
The area of a triangle with sides a, b and c can be expressed by
A = root{s(s-a)(s-b)(s-c)} with s being half the perimeter.
A beautiful aspect of this formula is, that a, b and c can be exchanged cyclically.
Is there an similar formula for the volume of a tetrahedron with edges a, b, c, d, e en f?
V=Ah/3 is far from sufficient.
2 Answers
- 1 decade agoFavorite Answer
the volume of a tetrahedron can also be expresse as the vector product o the three edges of the tetrahedron.
eg. a tetrahedron abcd with the base abc and edges ad,bd,cd the volume is the vector triple product of the three vectors ad,bd,cd. it can also be expressed in [ab,bd,cd]. this is also a cyclic function hence it can be expressed also as [bd,cd,ad] , [cd,ad,bd]. the solution to the vector triple product is the determinanat of the three vectors using unit vectors in the first column!
- Sherlock HolmesLv 61 decade ago
Yes it is also having the same type of formula. It will not be clear if it is written here so I am giving the site link. Click on it and view.
It will solve your problem
