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Pyramid

A polyhedron with a polygonal base and lateral faces that taper to an apex. A pyramid with a triangular base is called a tetrahedron.


Solid view: right regular pyramid with a regular pentagon as base

Frame view: right regular pyramid with a regular pentagon as base
For any pyramid: Volume = (1/3)(area of base)(height)
Lateral surface area for a right regular pyramid =
Total surface area for a right regular pyramid =
h = height of the pyramid
B = area of the base
P = perimeter of the base
s = slant height

All pyramids have the same volume formula. Here are some other types of pyramids:


Solid view: regular pyramid with a regular pentagon as base

Frame view: regular pyramid with a regular pentagon as base

Solid view: right pyramid with a square base

Frame view: right pyramid with a square base

Solid view: oblique pyramid with a square base

Frame view: oblique pyramid with a square base

 

See also

Area of a regular polygon, frustum of a cone or pyramid, volume

 


  this page updated 21-feb-16
Mathwords: Terms and Formulas from Algebra I to Calculus
written, illustrated, and webmastered by Bruce Simmons
NCTM Web Bytes December 2004 Web Bytes March 2005 Web Bytes