Hello,


This is my first time asking a question on this site so please let me know if I'm doing it wrong.


I have been trying to find out how to compute the hypervolume of an n-d simplex in an n+1 space.


I have found how to find the hypervolume of an n-d simplex in an n-d sapce, but don't know how to do it if the simplex is in an n+1 d space [link](http://www.mathpages.com/home/kmath664/kmath664.htm)


That link would show me how to compute the area of a triangle described in a 2-d space. I would need to know how to compute the area of a triangle described in a 3-d space. 


Thanks guys



Hypervolume of n-d simplex in an n+1 space
I am a bit conflicted, since this is not a research level question. However, the answer is nice:


1. Move one of the vertices to the origin.
2. if the remaining vertices are now $v\_1, \dots, v\_n$ find, by solving a linear system, the vector $v\_0$ orthogonal to all of the $v\_i.$ Normalize so that the norm of $v\_0$ equals $1.$
3. Find the volume of the simplex with vertices $0, v\_0, \dots, v\_n.$
4. Multiply by $n+1.$


