# Not Pythagoras Time

Geometry Level 4

$$ABCD$$ is a tetrahedron with a length of $$AB = 3, AC = 8, AD = 6, BC = 7, BD = 5$$ and $$CD = 4$$. If $$n$$ is the distance between the midpoint $$AB$$ and $$CD$$, then what is the value of $$n^2$$?

The brown shaded area is the surface area.

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