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use the formula for volume of irregular tetrahedral of given sides. first pair the given sides such that they don't have any common vertices. and name it (u,U),(v,V), (w,W) Volume = sqrt(4*u*u*v*v*w*w- u*u*sqr((v*v+w*w - U*U)) - v*v*sqr((w*w+u*u - V*V)) - w*w*sqr((u*u + v*v - W*W)) + (v*v +w*w - U*U)*(w*w+u*u- V*V)*(u*u+v*v - W*W))/12;

Also you can think in tartaglia theorem Determinant with: Leibniz and inversions with: fenwick tree.

Reference: http://www.cs.berkeley.edu/~wkahan/VtetLang.pdf