We are asked to find the sum of the number of faces, vertices, and edges of the above pyramid. Let's do it!
Therefore, the number of faces is 9, the number of vertices is 9, and the number of edges is 16. This tells us that the sum what we are looking for is 9+9+16=34.
Extra
General Approach
We will show also a general approach when we are dealing with an n-gonal pyramid.
Faces: There are n lateral faces and one base face. Therefore, the total number of faces is n+1.
Vertices: There are n base vertices and one top vertex. This tells us that the total number of vertices is n+1.
Edges: There are n base edges, and n lateral edges. Thus, the total number of edges is 2n.
Using the information above, when we substitute 8 for n we will get that the number of faces for an octagonal pyramid is 9, the number of vertices is 9, and the number of edges is 16.
