A regular tetrahedron has four equilateral triangles as faces. A regular square pyramid has four equilateral triangles and a square as faces. The faces of the tetrahedron are congruent to the triangular faces of the square pyramid.

A new polyhedron is created by gluing the tetrahedron and the square pyramid together at a triangular face so that the vertices of the triangles coincide. How many faces does this polyhedron have?

(In reply to

Surely not the intended solution ! by Syzygy)

if the triangles on the tetrahedron are the same size as the triangles of the square pyramid the angles are such that you create a "leaning" tetrahedron. 5 faces!