Area

{{otheruses1|the physical quantity}}
'''Area''' is a physical [[quantity]] expressing the size of a part of a [[surface]]. The term
'''Surface area''' is the summation of the areas of the exposed sides of an [[object (philosophy)|object]].

==Units==
Units for '''measuring surface area''' include:
:[[square metre]] = [[SI derived unit]]
:[[are]] = 100 square metres
:[[hectare]] = 10,000 square metres
:[[square kilometre]] = 1,000,000 square metres
:[[square megametre]] = 10<sup>12</sup> square metres
:[[square yard]] = 9 square feet = 0.83612736 square metres
:square [[perch (unit)|perch]] = 30.25 square yards = 25.2928526 square metres
:[[acre]] = 160 square perches or 43,560 square feet = 4046.8564224 square metres
:[[square mile]] = 640 acres = 2.5899881103 square kilometres

==Useful formulae==
[[Image:Area.svg|right|200px]]

{| class="prettytable"s
|+ Common [[equation]]s for area:
! Shape
! Equation
! Variables
|-
|[[Square (geometry)|Square]]
|<math>s^2\,\!</math>
|<math>s</math> is the length of the side of the square.
|-
|Regular [[hexagon]]
|<math>\frac{3 \sqrt{3}}{2}s^2\,\!</math>
|<math>s</math> is the length of one side of the hexagon.
|-
|Regular [[octagon]]
|<math>2(1+\sqrt{2})s^2\,\!</math>
|<math>s</math> is the length of one side of the octagon.
|-
|Any regular polygon
|<math>\frac{1}{2}a p \,\!</math>
|<math>a</math> is the [[apothem]], or the radius of an inscribed circle in the polygon, and <math>p</math> is the perimeter of the polygon.
|-
|Any regular polygon
|<math>\frac{P^2/n} {4 \cdot tan(\pi/n)}\,\!</math>
|<math>P</math> is the Perimeter and <math>n</math> is the number of sides.
|-
|Any regular polygon (using degree measure)
|<math>\frac{P^2/n} {4 \cdot tan(180^\circ/n)}\,\!</math>
|<math>P</math> is the Perimeter and <math>n</math> is the number of sides.
|-
|[[Rectangle]]
|<math>l \cdot w \,\!</math>
|<math>l</math> and <math>w</math> are the lengths of the rectangle's sides (length and width).
|-
|[[Parallelogram]] (in general)
|<math>b \cdot h\,\!</math>
|<math>b</math> and <math>h</math> are the length of the base and the length of the perpendicular height, respectively.
|-
|[[Rhombus]]
|<math>\frac{1}{2}ab</math>
|<math>a</math> and <math>b</math> are the lengths of the two [[diagonals]] of the rhombus.
|-
|[[Triangle]]
|<math>\frac{1}{2}b \cdot h \,\!</math>
|<math>b</math> and <math>h</math> are the [[Base (geometry)|base]] and [[Altitude (triangle)|altitude]] (measured perpendicular to the base), respectively.
|-
|[[Triangle]]
|<math>\frac{1}{2}\cdot a \cdot b \cdot sinC\,\!</math>
|<math>a</math> and <math>b</math> are any two sides, and <math>C</math> is the angle between them.
|-
|[[Circle]]
|<math>\pi r^2 \,\!</math>, or <math>\pi d^2/4 \,\!</math>
|<math>r</math> is the radius and <math>d</math> the [[diameter]].
|-
|[[Ellipse]]
|<math>\pi ab \,\!</math>
|<math>a</math> and <math>b</math> are the [[semi-major axis|semi-major]] and [[semi-minor axis|semi-minor]] axes, respectively.
|-
|[[Trapezoid]]
|<math>\frac{1}{2}(a+b)h \,\!</math>
|<math>a</math> and <math>b</math> are the parallel sides and <math>h</math> the distance (height) between the parallels.
|-
|Total surface area of a [[Cylinder (geometry)|Cylinder]]
|<math>2\pi r^2+2\pi r h \,\!</math>
|<math>r</math> and <math>h</math> are the radius and height, respectively.
|-
|Lateral surface area of a cylinder
|<math>2 \pi r h \,\!</math>
|<math>r</math> and <math>h</math> are the radius and height, respectively.
|-
|Total surface area of a [[Cone (geometry)|Cone]]
|<math>\pi r (l + r) \,\!</math>
|<math>r</math> and <math>l</math> are the radius and [[slant height]], respectively.
|-
|Lateral surface area of a cone
|<math>\pi r l \,\!</math>
|<math>r</math> and <math>l</math> are the radius and slant height, respectively.
|-
|Total surface area of a [[sphere (geometry)|Sphere]]
|<math>4\pi r^2\,\!</math> or <math>\pi d^2\,\!</math>
|<math>r</math> and <math>d</math> are the radius and diameter, respectively.
|-
|Total surface area of an [[ellipsoid (geometry)|ellipsoid]]
| 
|See the article.
|-
|[[Circular sector]]
|<math>\frac{1}{2} r^2 \theta \,\!</math>
|<math>r</math> and <math>\theta</math> are the radius and angle (in [[radians]]), respectively.
|-
|[[Square (geometry)|Square]] to circular area conversion
|<math>\frac{4}{\pi} A\,\!</math>
|<math>A</math> is the area of the [[square (geometry)|square]] in square units.
|-
|[[Circle|Circular]] to square area conversion
|<math>\frac{1}{4} C\pi\,\!</math>
|<math>C</math> is the area of the [[circle]] in circular units.

|}

==See also==
*[[Volume]]
*[[Orders of magnitude (area)]] — A list of areas by size.
*[[Real matrices (2 x 2)#Equi-areal mapping|Equi-areal mapping]]

==External links==
{{Wiktionary}}
*[http://www.sengpielaudio.com/calculator-cross-section.htm Conversion cable diameter to circle cross-sectional area and vice versa]
*[http://www.math.com/tables/geometry/areas.htm Area formulas]

[[Category:Area|*]]

[[af:Oppervlakte]]
[[als:Fläche]]
[[ar:مساحة]]
[[arc:ܫܛܝܚܘܬܐ]]
[[zh-min-nan:Biān-chek]]
[[be-x-old:Плошча]]
[[bg:Площ]]
[[ca:Àrea]]
[[cs:Obsah]]
[[cy:Arwynebedd]]
[[da:Areal]]
[[de:Flächeninhalt]]
[[et:Pindala]]
[[el:Έκταση]]
[[es:Área (geometría)]]
[[eo:Areo]]
[[eu:Azalera]]
[[fa:مساحت]]
[[fo:Vídd]]
[[fr:Superficie]]
[[gd:Farsaingeachd]]
[[gu:ક્ષેત્રફળ]]
[[ko:넓이]]
[[hr:Površina]]
[[io:Areo]]
[[ilo:Kalawa]]
[[id:Luas]]
[[is:Flatarmál]]
[[it:Area]]
[[he:שטח]]
[[ka:ფართობი]]
[[la:Area]]
[[lv:Platība]]
[[lb:Fläch]]
[[lt:Plotas]]
[[li:Oppervlak]]
[[ln:Etando]]
[[hu:Terület]]
[[mk:Плоштина]]
[[mg:Velarantany]]
[[ml:വിസ്തീര്‍ണ്ണം]]
[[ms:Keluasan]]
[[nl:Oppervlakte]]
[[ja:面積]]
[[no:Areal]]
[[nn:Flatevidd]]
[[oc:Superfícia]]
[[nds:Flach]]
[[pt:Área]]
[[ro:Suprafaţă]]
[[qu:Hallka k'iti k'anchar]]
[[ru:Площадь]]
[[sco:Area]]
[[simple:Area]]
[[sl:Površina]]
[[fi:Pinta-ala]]
[[sv:Ytmått]]
[[tl:Lawak]]
[[ta:பரப்பளவு]]
[[th:พื้นที่]]
[[vi:Diện tích]]
[[tr:Alan]]
[[uk:Площа]]
[[yi:שטח]]
[[zh-yue:面積]]
[[zh:面积]]