A regular tetrahedron (a solid with four faces) can be constructed from four unit-sided equilateral triangles.
Four similar triangles can also be assembled to have a common vertex and a unit-square base.
Adding that square creates a square pyramid (with five faces.)
These two solids can now be joined into another solid: by gluing together, vertex to vertex,
a triangular face from each of them.
How many faces does the joined solid have?