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.
2006-07-07 23:19:12 · 2 answers · asked by Thermo 6 in Science & Mathematics ➔ Mathematics
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!
2006-07-07 23:49:07 · answer #1 · answered by jivdex 2 · 1⤊ 0⤋
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
http://en.wikipedia.org/wiki/Tetrahedron#Area_and_volume
2006-07-08 07:15:16 · answer #2 · answered by Sherlock Holmes 6 · 0⤊ 0⤋