i have the lengths of 6 sides of a pyramid so how can i get its volume
the problem statment is:
https://www.spoj.pl/problems/PIR/
i have the lengths of 6 sides of a pyramid so how can i get its volume
the problem statment is:
https://www.spoj.pl/problems/PIR/
There is a straight-away answer but I don't know how in-depth it is. It's called Tartaglia's formula and can be found here Niccolò Fontana Tartaglia - Wikipedia, the free encyclopedia
So, let the vertices of the tetrahedron pyramid be 1,2,3 and 4. If $\displaystyle d_{i,j}= $ distance between vertices i and j, then these are just $\displaystyle d_{1,2},d_{1,3},d_{1,4},d_{2,3},d_{2,4},d_{3,4},$.
Then the volume is:
I don't know how one can derive it.