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Q: How many bases does a square pyramid?

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None!

A square pyramid has one base, and it is a square. That's why it's called a square pyramid. And because the base is a square, it has four sides.

A square pyramid has 1 square base and 4 triangle-shaped sides.

The base is the bottom, so a square-based pyramid has ONE base.

A square based pyramid has 8 edges, 6 vertices and 5 faces.

they both have square bases

While it is possible for a pyramid to have a square bases, you should not assume that all pyramids have square bases. Try to picture a triangular pyramid in your head, hopefully you can see that it is possible, and this would answer your question.

5. one for the square bottom, and one for each side coming out from the square

A square pyramid has five faces, one of which is a square and the remaining four are triangles. Conventionally such a pyramid is called a square BASED pyramid and in that context it has only one base. [That definition is used to distinguish it from a pentagonal pyramid, a hexagonal pyramid, etc.] However, any one of the five faces can be at the bottom.

5 faces one on the bottom and 4 for the sides

It is a pyramid that has a triangle as its base. The pyramids of Egypt are all built on square bases.

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