All ACT Math Resources
Example Question #6 : Tetrahedrons
Calculate the diagonal of a regular tetrahedron (all of the faces are equilateral triangles) with side length .
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.