Difference between revisions of "Pyramid"

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A '''pyramid''' is a 3-dimensional [[geometric solid]].  It consists of a [[base]] that is a [[polygon]] and a [[vertex]] in a plane other than the plane of the polygon.  The [[edge|edges]] of the pyramid are the [[side|sides]] of the polygonal base together with [[line segment|line segments]] connected the vertex of the pyramid to each vertex of the polygon.
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A '''pyramid''' is a 3-dimensional [[geometric solid]].  It consists of a [[base]] that is a [[polygon]] and a [[vertex]] not on the plane of the polygon.  The [[edge|edges]] of the pyramid are the [[side|sides]] of the polygonal base together with [[line segment|line segments]] connected the vertex of the pyramid to each vertex of the polygon.
  
 
The [[volume]] of a pyramid is given by the formula <math>\frac13bh</math>, where <math>b</math> is the area of the base and <math>h</math> is the [[height]].
 
The [[volume]] of a pyramid is given by the formula <math>\frac13bh</math>, where <math>b</math> is the area of the base and <math>h</math> is the [[height]].
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Some well-known pyramids include the [[tetrahedron]], which has an [[equilateral triangle]] for its base and all edges of equal length, and is one of the [[Platonic solids]]. Another is the regular square pyramid. Two of these with their bases joined form an [[octahedron]], which is another Platonic solid.
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If the base of the pyramid has <math>\displaystyle n</math> sides, then the pyramid has <math>\displaystyle 2n</math> edges, <math>\displaystyle n+1</math> vertices, and <math>\displaystyle n+1</math> faces (of which <math>\displaystyle n</math> are triangular, and the remaining one is the base). 
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== Problems ==
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=== Introductory ===
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=== Intermediate ===
  
 
{{WotW|week=Sep 6-12|prevweek=none|curweek=[[iTest]]<br />Pyramid|nextweek=TBA}}
 
{{WotW|week=Sep 6-12|prevweek=none|curweek=[[iTest]]<br />Pyramid|nextweek=TBA}}

Revision as of 16:31, 6 September 2007

This is an AoPSWiki Word of the Week for Sep 6-12

A pyramid is a 3-dimensional geometric solid. It consists of a base that is a polygon and a vertex not on the plane of the polygon. The edges of the pyramid are the sides of the polygonal base together with line segments connected the vertex of the pyramid to each vertex of the polygon.

The volume of a pyramid is given by the formula $\frac13bh$, where $b$ is the area of the base and $h$ is the height.

Some well-known pyramids include the tetrahedron, which has an equilateral triangle for its base and all edges of equal length, and is one of the Platonic solids. Another is the regular square pyramid. Two of these with their bases joined form an octahedron, which is another Platonic solid.

If the base of the pyramid has $\displaystyle n$ sides, then the pyramid has $\displaystyle 2n$ edges, $\displaystyle n+1$ vertices, and $\displaystyle n+1$ faces (of which $\displaystyle n$ are triangular, and the remaining one is the base).

Problems

Introductory

Intermediate

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