# Base (geometry)

Base (geometry)

The base of any geometric figure is (for polygons) any side that you wish to measure from or, (for polyhedra), any face that you wish to measure from. Bases are most commonly used in geometric formulas for area and volume. It is most commonly represented by the variable $b$. To distinguish side lengths from areas of bases in three-dimensional figures, the capital letter "B" often replaces "b" in signifying the area of a base.

Examples

The formula for the area of a triangle:

$A=frac\left\{1\right\}\left\{2\right\}bh,$

where $b$ is the length of the side from which you measure your perpendicular height ($h$).

The formula for the volume of a cone:

$V=frac\left\{1\right\}\left\{3\right\}Bh,$

The volume of the cone is the area of the base multiplied by one-third the height of the cone, where $B$ is the area of the circular face of the cone.

For many three-dimensional figures, including cylinders, prisms, and polyhedra, the volume is simply the area of the base multiplied by the figure's height:

V=Bh

It is important to note that a geometrical base is perspective-dependent. For example, there is no single base on a scalene triangle. The formula for the area will stay consistent, however, because the height of the triangle is also variable depending on which side of the triangle is chosen as the base. For equilateral triangles, each side is equal; it therefore does not matter from which side a height is measured.

For some three-dimensional figures there is only one base, e.g. a cone, or it does not matter which base is chosen, e.g. a right circular cylinder.

The base in geometry is essential to determining the volume of certain polyhedra. A highly irregular, concave polygon may be the base of a prism; if the area of that base is known, the volume of the prism is also known.

ee also

*Area
*Volume

Wikimedia Foundation. 2010.

### Look at other dictionaries:

• Geometry Wars — est une série de jeux vidéo créée par Bizarre Creations et éditée par Microsoft Game Studios, débutée en novembre 2003. Chaque titre de la série est un shoot them up multidirectionnel de type manic shooter au style graphique géométrique.… …   Wikipédia en Français

• Geometry Wars: Galaxies — Geometry Wars Geometry Wars Éditeur Microsoft Game Studios Genre Shoot them up multidirectionnel Début de la série Novembre 2003 Plate forme Nintendo DS Wii …   Wikipédia en Français

• Geometry Wars: Retro Evolved — Geometry Wars Geometry Wars Éditeur Microsoft Game Studios Genre Shoot them up multidirectionnel Début de la série Novembre 2003 Plate forme Nintendo DS Wii …   Wikipédia en Français

• Geometry Wars: Retro Evolved 2 — Geometry Wars Geometry Wars Éditeur Microsoft Game Studios Genre Shoot them up multidirectionnel Début de la série Novembre 2003 Plate forme Nintendo DS Wii …   Wikipédia en Français

• geometry — [jē äm′ə trē] n. pl. geometries [ME geometrie < OFr < L geometria < Gr geōmetria < geōmetrein, to measure the earth < gē, earth + metria, measurement < metrein, to measure: for IE base, see METER1] 1. the branch of mathematics… …   English World dictionary

• Base De Gröbner — Une base de Gröbner (ou base standard, ou base de Buchberger) d un idéal I de l anneau de polynômes est un ensemble de générateurs de cet idéal, vérifiant certaines propriétés supplémentaires. Cette notion a été introduite dans les années 1960,… …   Wikipédia en Français

• Base de Grobner — Base de Gröbner Une base de Gröbner (ou base standard, ou base de Buchberger) d un idéal I de l anneau de polynômes est un ensemble de générateurs de cet idéal, vérifiant certaines propriétés supplémentaires. Cette notion a été introduite dans… …   Wikipédia en Français

• Base de gröbner — Une base de Gröbner (ou base standard, ou base de Buchberger) d un idéal I de l anneau de polynômes est un ensemble de générateurs de cet idéal, vérifiant certaines propriétés supplémentaires. Cette notion a été introduite dans les années 1960,… …   Wikipédia en Français

• Base locus — In mathematics, specifically algebraic geometry, the base locus of a linear system of divisors on a variety refers to the subvariety of points common to all divisors in the linear system.More precisely, suppose that [D] is a linear system of… …   Wikipedia

• geometry — /jee om i tree/, n. 1. the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties… …   Universalium