Area 1209 224838943 2008-07-10T17:22:19Z ClueBot 4928500 Reverting possible vandalism by [[Special:Contributions/87.254.70.151|87.254.70.151]] to version by 24.199.91.88. False positive? [[User:ClueBot/FalsePositives|Report it]]. Thanks, [[User:ClueBot]]. (437089) (Bot) {{Mergefrom|Area (geometry)|date=February 2008}} {{otheruses1|the physical quantity}} '''Area''' is a [[quantity]] expressing the two-[[dimension]]al size of a defined part of a [[surface]], typically a region bounded by a closed [[curve]]. The term '''surface area''' refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a [[polyhedron]]. ==Units== Units for '''measuring surface area''' include: :[[Metric]] ::[[square metre]] (m²) = [[SI derived unit]] ::[[are]] (a) = 100 square metres (m²) ::[[hectare]] (ha) = 10,000 square metres (m²) ::[[square kilometre]] (km²) = 1,000,000 square metres (m²) ::[[square megametre]] (Mm²) = 10<sup>12</sup> square metres ::[[square foot]] = 144 square inches = 0.09290304 square metres (m²) ::[[square yard]] = 9 square feet = 0.83612736 square metres (m²) ::square [[perch (unit)|perch]] = 30.25 square yards = 25.2928526 square metres (m²) ::[[acre]] = 160 square perches or 4,840 square yards or 43,560 square feet = 4046.8564224 square metres (m²) ::[[square mile]] = 640 acres = 2.5899881103 square kilometres (km²) ==Useful formulas== [[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 [[triangle]] ||<math>\frac{\sqrt{3}}{4}s^2\,\!</math> ||<math>s</math> is the length of one side of the triangle. |- |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>lw \,\!</math> |<math>l</math> and <math>w</math> are the lengths of the rectangle's sides (length and width). |- |[[Parallelogram]] (in general) |<math>bh\,\!</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}bh \,\!</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} a b \sin C\,\!</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]] |&nbsp; |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. <!-- |- |A revolution of f(x) about the x-axis |<math>2 \pi \int_{a}^{b} |f(x)| \sqrt{1+(f'(x))^2}dx</math> |- |Area of surface of revolution of f(x) about the y-axis |<math>2 \pi \int_{a}^{b} |x| \sqrt{1+(f'(x))^2}dx</math> --> |} All of the above calculations show how to find the [[area]] of many [[shapes]]. The area of irregular polygons can be calculated using the "[[Surveyor's formula]]".<ref>[http://www.maa.org/pubs/Calc_articles/ma063.pdf]</ref> ==See also== *[[Real matrices (2 x 2)#Equi-areal mapping|Equi-areal mapping]] *[[Integral]] *[[Orders of magnitude (area)]]&mdash;A list of areas by size. *[[Volume]] ==External links== {{Wiktionary}} *[http://www.math.com/tables/geometry/areas.htm Area formulas] *[http://www.sengpielaudio.com/calculator-cross-section.htm Conversion cable diameter to circle cross-sectional area and vice versa] [[Category:Area|*]] [[af:Oppervlak]] [[als:Fläche]] [[ar:مساحة]] [[arc:ܫܛܝܚܘܬܐ]] [[zh-min-nan:Biān-chek]] [[be:Плошча]] [[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]] [[hi:क्षेत्रफल]] [[ko:넓이]] [[hr:Površina]] [[io:Areo]] [[ilo:Kalawa]] [[id:Luas]] [[ia:Superficie]] [[is:Flatarmál]] [[it:Area]] [[he:שטח]] [[ka:ფართობი]] [[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]] [[pl:Powierzchnia]] [[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]]