One square and four triangles.
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Pyramids are a type of polyhedron that has a polygonal base with triangles extending from it to form an apex. The pyramids of Egypt would be examples of square pyramids because the bottom of them are squares. Likewise, you could have a pentagonal pyramid, hexagonal pyramid, pentagrammic pyramid etc.
A square pyramid has 5 faces. The four side faces are triangles, and the base is in the form of a square. This pyramid has 5 vertices and 8 edges.
Yes, Some can even be formed into a square and two triangles or a rectangle and one or two triangles. Just drop perpendicular(s) from the vertex (vertices) of the short side to the long side (that is to say, the two sides which are parallel). That will form one or two right triangles and a rectangle of some sort...could be a square--all squares are rectangles but not all rectangles are squares.
Well, honey, with 2 squares and 2 triangles, you can make a lovely little house shape. Just slap those squares together for the base, and plop those triangles on top for the roof. Voila! You've got yourself a cute little geometric abode.
An octagonal pyramid has 9 vertices. The base of this shape is an octagon, which will give it 8 vertices when the triangles that form the sides are considered. Those triangles will lead up to the apex (top) of the pyramid, and that will be the 9th vertex.