How to find the diagonal of a tetrahedron

The diagonal of a shape is simply the length from a vertex to the center of the face or vertex opposite to it. With a regular tetrahedron, we have a face opposite to the vertex, and this basically amounts to calculating the height of our shape.

We know that the height of a tetrahedron is where s is the side length, so we can put into this formula:

which gives us the correct answer.