Tetrahedron Volume

Geometry Level 5

Tetrahedron ABCDABCD has side lengths AB=CD=12AB=CD=12, and these edges are perpendicular to each other. Let EE and FF be the midpoints of ABAB and CDCD respectively. We are given that EF=10EF= 10 and is perpendicular to both ABAB and CDCD. What is the volume of ABCDABCD?

Details and assumptions

In 3 dimensions, perpendicular lines do not need to intersect. For example, the line l1:z=0,y=0l_1 : z=0, y=0 is perpendicular to the line l2:y=1,x=1 l_2 : y=1, x=1.

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