# Tetrahedron Volume

Geometry Level 5

Tetrahedron $$ABCD$$ has side lengths $$AB=CD=12$$, and these edges are perpendicular to each other. Let $$E$$ and $$F$$ be the midpoints of $$AB$$ and $$CD$$ respectively. We are given that $$EF= 10$$ and is perpendicular to both $$AB$$ and $$CD$$. What is the volume of $$ABCD$$?

Details and assumptions

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

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