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Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. The surface area of a 3-dimensional solid is the total area of the exposed surface, such as the sum of the areas of the exposed sides of a polyhedron. Area is an important invariant in the differential geometry of surfaces.1
Contents 1 Units 2 Formulae 3 Additional formulae 3.1 Areas of 2-dimensional figures 3.2 Area in calculus 3.3 Surface area of 3-dimensional figures 3.3.1 General formula 4 Minimization 5 See also 6 References 6.1 Notes 7 External links // UnitsUnits for measuring area, with exact conversions, include:
square metre (m2) are (a) = 100 square metres (m2) hectare (ha) = 100 ares = 10000 square metres square kilometre (km2) = 100 hectares = 10000 ares = 1000000 square metres square megametre (Mm2) = 1000000000000 square metres square foot = 144 square inches = 0.09290304 square metres square yard = 9 square feet = 0.83612736 square metres square perch = 30.25 square yards = 25.2928526 square metres acre = 10 square chains = one furlong by one chain = 160 square perches = 4840 square yards = 43560 square feet = 4046.8564224 square metres square mile = 640 acres = 2.589988110336 square kilometres Kanal (unit) = 0.125 acres. Formulae Common formulae for area: Shape Formula Variables Regular triangle (equilateral triangle) s is the length of one side of the triangle. Triangle s is half the perimeter, a, b and c are the length of each side. Triangle a and b are any two sides, and C is the angle between them. Triangle b and h are the base and altitude (measured perpendicular to the base), respectively. Square s is the length of one side of the square. Rectangle l and w are the lengths of the rectangle's sides (length and width). Rhombus a and b are the lengths of the two diagonals of the rhombus. Parallelogram b is the length of the base and h is the perpendicular height. Trapezoid a and b are the parallel sides and h the distance (height) between the parallels. Regular hexagon s is the length of one side of the hexagon. Regular octagon s is the length of one side of the octagon. Regular polygon s is the sidelength and n is the number of sides. a is the apothem, or the radius of an inscribed circle in the polygon, and p is the perimeter of the polygon. Circle r is the radius and d the diameter. Circular sector r and θ are the radius and angle (in radians), respectively. Ellipse a and b are the semi-major and semi-minor axes, respectively. Total surface area of a Cylinder r and h are the radius and height, respectively. Lateral surface area of a cylinder r and h are the radius and height, respectively. Total surface area of a Cone r and l are the radius and slant height, respectively. Lateral surface area of a cone r and l are the radius and slant height, respectively. Total surface area of a Sphere r and d are the radius and diameter, respectively. Total surface area of an ellipsoid See the article. Total surface area of a Pyramid B is the base area, P is the base perimeter and L is the slant height. Square to circular area conversion A is the area of the square in square units. Circular to square area conversion C is the area of the circle in circular units.The above calculations show how to find the area of many common shapes.
The area of irregular polygons can be calculated using the "Surveyor's formula".2
Additional formulae Areas of 2-dimensional figures a triangle: (where B is any side, and h is the distance from the line on which B lies to the other vertex of the triangle). This formula can be used if the height h is known. If the lengths of the three sides are known then Heron's formula can be used: (where a, b, c are the sides of the triangle, and is half of its perimeter) If an angle and its two included sides are given, then area=absinC where C is the given angle and a and b are its included sides. If the triangle is graphed on a coordinate plane, a matrix can be used and is simplified to the absolute value of (x1y2+ x2y3+ x3y1 - x2y1- x3y2- x1y3) all divided by 2. This formula is also known as the shoelace formula and is an easy way to solve for the area of a coordinate triangle by substituting the 3 points, (x1,y1) (x2,y2) (x3,y 3). The shoelace formula can also be used to find the areas of other polygons when their vertices are known. Another approach for a coordinate triangle is to use Infinitesimal calculus to find the area. a simple polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon's vertices are grid points: , where i is the number of grid points inside the polygon and b is the number of boundary points. This result is known as Pick's theorem. Area in calculus The area between two graphs can be evaluated by calculating the difference between the integrals of the two functions the area between the graphs of two functions is equal to the integral of one function, f(x), minus the integral of the other function, g(x). an area bounded by a function r = r(θ) expressed in polar coordinates is . the area enclosed by a parametric curve with endpoints is given by the line integrals(see Green's theorem)
or the z-component of Surface area of 3-dimensional figures cube: 6s2, where s is the length of the top side rectangular box: the length divided by height cone: , where r is the radius of the circular base, and h is the height. That can also be rewritten as πr2 + πrl where r is the radius and l is the slant height of the cone. πr2 is the base area while πrl is the lateral surface area of the cone. prism: 2 × Area of Base + Perimeter of Base × Height General formulaThe general formula for the surface area of the graph of a continuously differentiable function z = f(x,y), where and D is a region in the xy-plane with the smooth boundary:
Even more general formula for the area of the graph of a parametric surface in the vector form where is a continuously differentiable vector function of :
1 MinimizationGiven a wire contour, the surface of least area spanning ("filling") it is a minimal surface. Familiar examples include soap bubbles.
The question of the filling area of the Riemannian circle remains open.
See also Equi-areal mapping Integral Orders of magnitude (area)—A list of areas by size. Volume References Notes ^ a b do Carmo, Manfredo. Differential Geometry of Curves and Surfaces. Prentice-Hall, 1976. Page 98. ^ http://www.maa.org/pubs/Calc_articles/ma063.pdf External links Look up area in Wiktionary, the free dictionary. Area formulas Conversion cable diameter to circle cross-sectional area and vice versaArea | Define Area at Dictionary.com
Area definition, any particular extent of space or surface; part: See more.
dictionary.reference.com/browse/area
Area definition, any particular extent of space or surface; part: See more.
dictionary.reference.com/
NOT JUST A VACATION IT S AN EXPERIENCE Imagine tranquil lakes and gentle streams as well as rushing whitewater all surrounded by the lush Cherokee National Forest in eastern
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Content Area Reading: Literacy and Learning Across the Curriculum (9th Edition) Allyn & Bacon
area: Definition, Synonyms from Answers.com
(Click to enlarge) area To calculate the area of a rectangle, multiply the length by the width. The area of this rectangle is 50 square feet
www.answers.com/topic/area
(Click to enlarge) area To calculate the area of a rectangle, multiply the length by the width. The area of this rectangle is 50 square feet
www.answers.com/topic/area
Area police ready for traffic crackdown
Area police will be beefing up their presence on local roads and waterways throughout Labour Day weekend and into the first week of school.[...]
Area police will be beefing up their presence on local roads and waterways throughout Labour Day weekend and into the first week of school.[...]
Here is us working on the area and the finished product Spring 2007 I picked 2 colors of stain that will be carried throughout the area and I layed down some sod and stepping stones within the area The 6×6 posts enclose the seating area and
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CONTENT AREA LITERACY: AN INTEGRATED APPROACH Kendall Hunt Publishing
area - definition of area by the Free Online Dictionary ...
Translations of area. area synonyms, area antonyms. Information about area in the free online English dictionary and encyclopedia. surface area ...
www.thefreedictionary.com/area
Translations of area. area synonyms, area antonyms. Information about area in the free online English dictionary and encyclopedia. surface area ...
www.thefreedictionary.com/area
Capital Area Michigan Works' $250,000 grant to boost area biomanufacturing
Capital Area Michigan Works has landed a $250,000 grant to help bolster the region's biomanufacturing sector.
Capital Area Michigan Works has landed a $250,000 grant to help bolster the region's biomanufacturing sector.
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Subjects Matter: Every Teacher's Guide to Content-Area Reading Heinemann
The Area :: Homepage
... downloads, movie and image galleries, professional industry artist interviews and job posting boards. AREA members also have access to Product-specific ...
area.autodesk.com
... downloads, movie and image galleries, professional industry artist interviews and job posting boards. AREA members also have access to Product-specific ...
area.autodesk.com
Area firms cited by EPA
The feds have ordered three area firms to halt the handling and processing of hazardous materials that had caused contamination. The Environmental Protection Agency issued the order for TNT General Contracting of Kahoka, the Carl and Carol Trump Trust of Kahoka and Webb Minerals LLC of Quincy, Ill.
The feds have ordered three area firms to halt the handling and processing of hazardous materials that had caused contamination. The Environmental Protection Agency issued the order for TNT General Contracting of Kahoka, the Carl and Carol Trump Trust of Kahoka and Webb Minerals LLC of Quincy, Ill.
Heise's Plumbing, San Francisco CA
Content-Area Writing: Every Teacher's Guide Heinemann
area - Wiktionary
Wikipedia area (plural areas or areæ) (mathematics) A measure of the extent of a planar region, or of the surface of a solid; it is measured in square units ...
en.wiktionary.org/wiki/area
Wikipedia area (plural areas or areæ) (mathematics) A measure of the extent of a planar region, or of the surface of a solid; it is measured in square units ...
en.wiktionary.org/wiki/area
Dallas-area man blames shooting range for wound
A Dallas-area man with a bullet in his back is suing a mile-away shooting range.
A Dallas-area man with a bullet in his back is suing a mile-away shooting range.
Winter Tour of Wellnesste Lodge
Clinical Calculations: With Applications to General and Specialty Areas Saunders
Welcome to Area, Inc. :: New York
Area is a small New York-based textile company with emphasis on ease, durability and natural beauty Area duvets, sheets, blankets and tabletop
areahome.com
Area is a small New York-based textile company with emphasis on ease, durability and natural beauty Area duvets, sheets, blankets and tabletop
areahome.com
Area groups receive cultural grants
Area projects are among 22 organizations receiving grantstotaling $51,061.
Area projects are among 22 organizations receiving grantstotaling $51,061.
Bay Area Condominiums Bay Area Realtor
Home for Sale: 0 Unit 26 Block 8lot 56/57 - MLS: ...
Reading to Learn in the Content Areas Wadsworth Publishing
AREA
AREA provides decision makers at the national, ... AREA is organized for educational purposes. AREA members include representatives of State, Federal, industry, ...
www.areanet.org
AREA provides decision makers at the national, ... AREA is organized for educational purposes. AREA members include representatives of State, Federal, industry, ...
www.areanet.org
Boone Area Soccer Club kicks off new season
The Boone Area Soccer Club kicked off its seventh season this past weekend with games being played in five separate divisions.
The Boone Area Soccer Club kicked off its seventh season this past weekend with games being played in five separate divisions.
Pictures
Home for Sale: 9801 Admiral Dewey Ave NE - MLS: 692016
Safe Area Gorazde: The War in Eastern Bosnia 1992-1995 Fantagraphics Books
Area – Free listening, videos, concerts, stats, & pictures at ...
Area is a name shared by many artists: An Italian avant-progressive and free-jazz/fusion ... 1) Area is an Italian avant-progressive and free-jazz/fusion band formed in the ...
www.last.fm/music/Area
Area is a name shared by many artists: An Italian avant-progressive and free-jazz/fusion ... 1) Area is an Italian avant-progressive and free-jazz/fusion band formed in the ...
www.last.fm/music/Area
Area football previews 09/03/10
Brief previews of Pantagraph-area high school football games tobe played on Sept. 2.
Brief previews of Pantagraph-area high school football games tobe played on Sept. 2.
lion's mane jellyfish
Content Area Reading: Teaching and Learning in an Age of Multiple Literacies (with MyEducationLab) Allyn & Bacon
Bay Area travelers ready for holiday gambol
As thousands of Bay Area travelers prepare to hit the road this Labor Day weekend, they have a lot to contend with -- a hurricane named Earl expected to disrupt air travel along the East Coast, and major roadwork along Interstates 80 and 680.
As thousands of Bay Area travelers prepare to hit the road this Labor Day weekend, they have a lot to contend with -- a hurricane named Earl expected to disrupt air travel along the East Coast, and major roadwork along Interstates 80 and 680.
Home for Sale: 4716 Hannett Ave NE - MLS: 686978
Content Area Reading and Writing: Fostering Literacies in Middle and High School Cultures (2nd Edition) Prentice Hall
Vacaville area athletes all over college football, especially at Sac State
Vacaville area football players are on college rosters from coast to coast, but none come in a bigger bunch than on the campus at Sacramento State.
Vacaville area football players are on college rosters from coast to coast, but none come in a bigger bunch than on the campus at Sacramento State.
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Bairds Creek Green Bay Triangle Hill Sports Area