The Volume of a Tetrahedron in Terms of its Six Edges

Abstract

Before applying our method to a tetrahedron, let us consider the case of a triangle ABC, whose vertices are (x₁,y₁) (x₂,y₂) (x₃,y₃). The determinant

|x₁²+y₁²   x₁   y₁   1

x₂²+y₂²   x₂   y₂   1

x₃³+y₃³   x₃   y₃   1

     1       0      0     c|