# The Minimum Possible Surface Area of A Tetrahedron with A Fixed Face and Volume

Geometry Level 5

Let $$ABC$$ be a triangle such that $$BC=13$$, $$CA=14$$, and $$AB=15$$. Furthermore, let $$D$$ be a point in space such that the volume of tetrahedron $$ABCD$$ is $$28$$. The minimum possible surface area of tetrahedron $$ABCD$$ can be expressed in the form $$p\sqrt{q}+r$$, where $$p$$ and $$r$$ are positive integers and $$q$$ is a squarefree integer. Find $$p+q+r$$.

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