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Pyramid

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 of a right regular pyramid with a yellow pentagonal base and four triangular lateral faces tapering to an apex.
Solid view: right regular pyramid with a regular pentagon as base		 Solid view of a right regular pyramid with a pentagonal base, showing height h and slant height s labeled in red.
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 = Formula: one-half times P times s
Total surface area for a right regular pyramid = B + (1/2)Ps, formula for total surface area of a right regular pyramid, where B is base area, P is perimeter, s is slant height.
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 of a right regular pyramid with a regular pentagon base, shown in yellow-green with shaded lateral faces tapering...
Solid view: regular pyramid with a regular pentagon as base		 Solid view of a right regular pyramid with a pentagonal base and red vertical height labeled h from apex to base.
Frame view: regular pyramid with a regular pentagon as base
3D solid view of a right regular pyramid with a square base, showing a yellow front face and dark olive side face with an apex.
Solid view: right pyramid with a square base		 3D pyramid with square base and apex connected by triangular faces; height labeled h shown as vertical dashed line.
Frame view: right pyramid with a square base
Solid view of an oblique pyramid with a square base, apex shifted off-center, shown in yellow and dark olive green.
Solid view: oblique pyramid with a square base		 Solid view of an oblique pyramid with a square base, apex offset from center, and height labeled h.
Frame view: oblique pyramid with a square base

 

See also

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