Commandino's theorem states:
The four medians of a tetrahedron are concurrent at a point S, which divides them in a 3:1 ratio. A median is any line segment that connects a vertex to the centroid of the opposite face. Point S is also the centroid of the tetrahedron.
I don't urgently need the proof to Commandino's theorem, I just want to understand it works. I have seen some proofs online, but I can't make any sense of them. One of the proofs I found came from a paper titled: On the Centroids of Polygons and Polyhedra. I think that it may be obvious why this proof is beyond me if you take a cursory glance at it (it's a lot of information). I came here hoping that someone will be able to provide a simpler proof, or restate the proof in a way that is easier to understand. I'm in 8th grade geometry.
I used Commandino's theorem to help solve the problem:
Given a regular tetrahedron with edge length 8, find the area of the cross section that contains the intersection of the altitudes of the tetrahedron.