The bottom, or base of a pyramid would count as a face is you were finding out surface area.
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That is how a pyramid is defined!That is how a pyramid is defined!That is how a pyramid is defined!That is how a pyramid is defined!
The lateral face for a prism or pyramid is any edge or face which is not part of a base.
24 faces including the base face
An octagonal pyramid has 9 faces and 14 edges. The base of the pyramid is an octagon with 8 faces, and the pyramid itself has an additional triangular face. The edges consist of the edges of the octagon base and the edges connecting the base to the apex of the pyramid.
The most common pyramid shapes have 3 faces on a triangular base or 4 faces on a square face. Other pyramid shapes may have more faces corresponding to the shape of the base.