A side and face of a three-dimensional object are the same thing.
A pyramid is a generic term. It refers to a solid object with a polygonal face - with n number of sides (n > 2) - and n triangular faces that meet at an apex. So a pyramid can have 4 or more faces.
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A rectangular pyramid has five faces. Sides are the same things as faces. A pyramid with a triangular base has 4 faces. This is the more common type of pyramid in mathematics, as it is a platonic solid.
Faces = sides = 5. Edges = 8
The sides of a pyramid are known in geometry as faces.
If the base is a polygon with n sides, the pyramid will have n+1 faces. Triangle base (3 sides) gives 5 faces, Quadrilateral base (4 sides) has 5 faces, etc.
There are 4 faces but 5 sides (don't forget the bottom).