Thread: how can i get volume of pyramid from its sides lengths

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 [LaTeX ERROR: Convert failed] distance between vertices i and j, then these are just [LaTeX ERROR: Convert failed] .

Then the volume is:



I don't know how one can derive it.

thx for reply and i want to know ideas of all members here