2-piece 4-piece pyramid

Combine the two blue pieces to make a pyramid. Hint: What happens to the square face of each piece?

Combine the four red pieces to make a pyramid. Hint: Two small red pieces can be put together to form a piece of the blue pyramid.

With the 4-piece puzzle we can see one cross-section of the tetrahedron is a square. What is the other cross section?

The 2-piece pyramid is made from two identical pieces. Since a tetrahedron only has triangular faces, the square faces of the 2-piece pyramid have to vanish. This can be achieved by putting the square faces together. In other words, the square is hidden inside the tetrahedron. In fact, it is a cross-section of the tetrahedron. The four edges of the square lie on each of the four faces of the tetrahedron.

The 4-piece pyramid is made from four identical pieces. However, we can put two red pieces together to form an object which looks like a blue piece, and solve as before. In this case we can see one cross-section of the tetrahedron is a square, and another cross-section of the tetrahedron is a triangle.