I know a nice proof of volume of tetrahedron being 1/3 of the corresponding paralellepiped. You split it into smaller tetrahedra by midpoints and count them. A

I know a nice proof of volume of tetrahedron being 1/3 of the corresponding paralellepiped. You split it into smaller tetrahedra by midpoints and count them. Also there is a nice visual proof that in an equilateral triangle, for every point in it, the sum of distances from all the sides is constant.