The base of the pyramid is a polygon with n sides. How many faces does it have? What about if the polyhedron is a prism?
Example Solution: A hexagonal pyramid and a pentagonal prism.
Practice makes perfect
Notice that if the base of a pyramid is a polygon with n sides, it will have n+1 faces — namely, one for each side plus the base. Since we want a polyhedron with 7 faces, let's equate these two quantities and solve it for n.
n+1 = 7 ⇒ n=6
Therefore, a hexagonal pyramid is a polyhedron with 7 faces.
On the other hand, a prism whose bases are polygons with n sides has n+2 faces — one for each side plus the two bases. Again, let's equate this quantity and 7 and solve it for n.
n+2 = 7 ⇒ n=5
In consequence, a pentagonal prism is a polyhedron with 7 faces. Keep in mind that there are more polyhedrons with 7 faces and so, your answer may vary.
