Pyramids

A pyramid is a polyhedron for which one face, called the base, is a polygon and all other faces, called lateral faces, are triangles.  As with prisms, pyramids are often classified by the shapes of their bases.  Thus a triangular pyramid is one in which the base is a triangle and a square pyramid is one in which the base is a square.  If the base is the "bottom" of the pyramid, the "top point" is called its apex.  If the base is a regular polygon and all the faces are congruent isosceles triangles, then the pyramid is called a regular pyramid.

 

The segment from the apex perpendicular to the base of a pyramid is called its altitude.  Sometimes the length of this segment is also called the altitude.  In a regular pyramid, a segment from the apex perpendicular to a side of the base (or the length of that segment) is called the slant height.

 

 

The lateral surface area of a pyramid is the total area of its lateral faces.  For a regular pyramid, this area is equal to ½ of the slant height times the perimeter of the base.

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