Can you solve the tetrahedron math puzzle? You have a tetrahedron and a pyramid with equal side lengths. A tetrahedron is made up of four equilateral triangles (a total of four sides), and a pyramid is made up of four equilateral triangles and a square base (a total of five sides). The two shapes are glued together on a triangular face. How many faces are there on the resulting figure? This was on a 1980 PSAT math exam question... and many people got it wrong.