Area - Revision history

Antefyn: A few minor fixes

2015-09-27T10:15:47Z

A few minor fixes

Antefyn: Minor fixes in first paragraph

2015-09-27T07:56:32Z

Minor fixes in first paragraph

← Older revision		Revision as of 02:56, 27 September 2015
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	'''Area''' is the [[content]] of a [[planespace\|two-dimensional]] [[manifold]] (a [[surface]]), corresponding to the [[length]] in [[linespace\|one dimension]], to [[volume]] in [[realmspace\|three dimensions]], and to [[bulk]] in [[flunespace\|four]]. Roughly speaking, [[area]] can be ~~though~~ of as the "size" of the [[manifold]], or as the amount of "material" that it would take to cover the manifold completely.		'''Area''' is the [[content]] of a [[planespace\|two-dimensional]] [[manifold]] (a [[surface]]), corresponding to the [[length]] in [[linespace\|one dimension]], to [[volume]] in [[realmspace\|three dimensions]], and to [[bulk]] in [[flunespace\|four]]. Roughly speaking, area can be thought of as the "size" of the [[manifold]], or as the amount of "material" that it would take to cover the manifold completely.

	While area is fundamentally a two-dimensional property, it is possible to define an area associated with a three-dimensional manifold (a [[cast]]). One important such area is the [[surface area]], the area of the (two-dimensional) [[boundary]] of a cast. (The name is a bit misleading, perhaps, because all areas pertain to surfaces by definition.) Another is the [[cross section]]al area, the area of the intersection of the manifold with a [[plane]] (or, more rarely, with some other two-dimensional shape). Unlike the surface area, the cross-sectional area of a three-dimensional manifold is not uniquely defined; it depends on the particular two-dimensional manifold the three-dimensional manifold is intersected with, as well as where and at what [[angle]] the intersection takes place. Often a planar cross section is taken where the area is largest, but this is not a universal standard.		While area is fundamentally a two-dimensional property, it is possible to define an area associated with a three-dimensional manifold (a [[cast]]). One important such area is the [[surface area]], the area of the (two-dimensional) [[boundary]] of a cast. (The name is a bit misleading, perhaps, because all areas pertain to surfaces by definition.) Another is the [[cross section]]al area, the area of the intersection of the manifold with a [[plane]] (or, more rarely, with some other two-dimensional shape). Unlike the surface area, the cross-sectional area of a three-dimensional manifold is not uniquely defined; it depends on the particular two-dimensional manifold the three-dimensional manifold is intersected with, as well as where and at what [[angle]] the intersection takes place. Often a planar cross section is taken where the area is largest, but this is not a universal standard.

Antefyn at 07:53, 27 September 2015

2015-09-27T07:53:02Z

← Older revision		Revision as of 02:53, 27 September 2015
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	* [[Wikipedia:Quinaria\|Quinaria]]: A unit of area used in ancient [[Rome]] to measure the cross-sectional area of a pipe, equal to about 4.5 square centimeters.		* [[Wikipedia:Quinaria\|Quinaria]]: A unit of area used in ancient [[Rome]] to measure the cross-sectional area of a pipe, equal to about 4.5 square centimeters.
	* [[Wikipedia:Stremma\|Stremma (στρέμμα)]]*: A unit of measurement originating in ancient [[Greece]], still used but now standardized to exactly 1,000 square meters.		* [[Wikipedia:Stremma\|Stremma (στρέμμα)]]*: A unit of measurement originating in ancient [[Greece]], still used but now standardized to exactly 1,000 square meters.
	* [[Wikipedia:Japanese units of measurement#Area\|Tsubo (坪)]]: A [[Japan]]ese unit of area defined as the area of two [[Wikipedia:tatami\|tatami]] mats, and standardized as equal to about 3.306 meters. An equivalent unit used in [[agriculture]] is a ''bu'' (歩). Various fractions and multiples of the ''tsubo''/''bu'' have their own names: 1/100 of a ''tsubo'' is a ''shaku'' (勺), 1/10 is a ''g&#~~x0143~~;'' (合), 1/2 a ''j&#~~x0143~~;'' (畳); 30 ''bu'' are a ''se'' (畝), 300 a ''tan'' (段/反), and 3,000 a ''ch&#~~x0143~~;'' (町/町歩).		* [[Wikipedia:Japanese units of measurement#Area\|Tsubo (坪)]]: A [[Japan]]ese unit of area defined as the area of two [[Wikipedia:tatami\|tatami]] mats, and standardized as equal to about 3.306 meters. An equivalent unit used in [[agriculture]] is a ''bu'' (歩). Various fractions and multiples of the ''tsubo''/''bu'' have their own names: 1/100 of a ''tsubo'' is a ''shaku'' (勺), 1/10 is a ''gō'' (合), 1/2 a ''jō'' (畳); 30 ''bu'' are a ''se'' (畝), 300 a ''tan'' (段/反), and 3,000 a ''chō'' (町/町歩).
	[[Category:Contents]]		[[Category:Contents]]

Antefyn: Created page with "'''Area''' is the content of a two-dimensional manifold (a surface), corresponding to the length in one dimension, to volume i..."

2015-09-27T07:49:22Z

Created page with "'''Area''' is the content of a two-dimensional manifold (a surface), corresponding to the length in one dimension, to volume i..."

New page

'''Area''' is the [[content]] of a [[planespace|two-dimensional]] [[manifold]] (a [[surface]]), corresponding to the [[length]] in [[linespace|one dimension]], to [[volume]] in [[realmspace|three dimensions]], and to [[bulk]] in [[flunespace|four]]. Roughly speaking, [[area]] can be though of as the "size" of the [[manifold]], or as the amount of "material" that it would take to cover the manifold completely.

While area is fundamentally a two-dimensional property, it is possible to define an area associated with a three-dimensional manifold (a [[cast]]). One important such area is the [[surface area]], the area of the (two-dimensional) [[boundary]] of a cast. (The name is a bit misleading, perhaps, because all areas pertain to surfaces by definition.) Another is the [[cross section]]al area, the area of the intersection of the manifold with a [[plane]] (or, more rarely, with some other two-dimensional shape). Unlike the surface area, the cross-sectional area of a three-dimensional manifold is not uniquely defined; it depends on the particular two-dimensional manifold the three-dimensional manifold is intersected with, as well as where and at what [[angle]] the intersection takes place. Often a planar cross section is taken where the area is largest, but this is not a universal standard.

Area is usually abbreviated ''A'', though surface area is often abbreviated ''S'' instead.

==Calculations==
The area of a shape can be determined the same way as for other-dimensional contents. Known formulæ exist for some widely used shapes, while determining the area of an arbitrary shape for which no formula is known may require [[calculus]].

===Formulæ===
There are some [[shape]]s for which the area can be [[calculation|calculated]] through relatively simple formulæ. The area of a [[circle]] of [[radius]] ''r'' is <math>2 \pi r</math>; the area of an [[ellipse]] of radii ''a'' and ''b'' is simply <math>\pi a b</math> (of which formula the circle formula may be taken as a special case). Even more generally, the area of a [[superellipse]] of radii ''a'' and ''b'' and of [[exponent]] <math>n</math> is equal to <math>4 a b \frac{(\Gamma ( 1 + \frac {1}{n} ) )^2}{\Gamma (1 + \frac {2}{n} ) }</math>.

The area of a [[regular polygon]] of ''n'' sides each of length ''s'' is <math>\frac{1}{4} n s^2 \cot (\frac {\pi}{n})</math>. The area of a [[rectangle]] is just the product of its length and width. As a special case of both formulae, the area of a [[square (geometry)|square]] of side length ''s'' is <math>s^2</math>. The area of a [[triangle]] is generally given as <math>\frac{1}{2} b h</math>, with ''b'' and ''h'' respectively its base and height, but there are other forms of this formula for other information, such as [[Hero's formula]] when the lengths of the three sides of the triangle are known. The area of an arbitrary polygon, as long the [[coordinate]]s of its [[vertex|vertices]] are known, can be derived through an [[expression]] sometimes called the [[shoelace formula]].

The area of a [[lemniscate]] with a focal distance of <math>a</math> is simply <math>a^2</math>. The area of the [[rose (geometry)|rose]] <math>r = a \sin n \theta</math>, <math>n \in Z^+</math>, is equal to <math>\frac {\pi a^2}{2}</math> if <math>n</math> is even, and <math>\frac {\pi a^2}{4}</math> if <math>n</math> is odd. The area of a loopless [[limaçon]] <math>r = b + a \cos \theta</math> with <math>b <= a</math> is equal to <math>\frac{\pi}{2} ( a^2 + 2 b^2)</math>; when <math>b = a</math> this becomes a [[cardioid]], and the area reduces to <math>\frac{3}{2} a^2</math>. For a limaçon with a loop (when <math>b > a</math>), the area of the loop is <math>\frac{1}{2}( a^2 + 2 b^2 )\cos^{-1} \frac{b}{a} - \frac {3}{2} b \sqrt{a^2 - b^2}</math>, and the area of the rest of the limaçon is <math>( a^2 + 2 b^2)\sin^{-1} \frac{b}{a} + 3 b \sqrt{a^2 - b^2}</math>.

While the above formulæ all deal with [[flat]] shapes, formulæ can of course be derived for areas of curved surfaces as well. The area of a [[spherical triangle]] on a sphere of radius ''R'', for example, can be written as <math>A = R^2 (A + B + C - \pi)</math>, where ''A'', ''B'', and ''C'' are the triangle's vertex angles in [[radian]]s.

===Integration===
While formulæ exist for these special cases, the area of an arbitrary shape can be found through methods of [[calculus]] (which is in fact how most of these formulæ can be derived). In a [[flat]] two-dimensional [[plane (geometry)|plane]], the area under a [[curve]] (that is, between the curve and the [[x axis]]) can be found by [[integrating]] the [[equation]] of the curve over the [[x coordinate]]. For example, if we wanted to find the area under the [[parabola]] <math>y = -x^2+4</math> between <math>x=-2</math> and <math>x=2</math>, we would integrate <math>A = \int_{2}^{2} (-x^2+4) dx = \left [ -\frac{1}{3}x^3 + 4x \right ]_-2^2 = \left (-\frac{8}{3} + 8 \right ) - \left (\frac{8}{3} - 8 \right ) = \frac{32}{3}</math>. The area between two curves <math>f(x)</math> and <math>g(x)</math> is simply the integral of the difference of the areas under each curve, <math>\int \left ( f(x) - g(x) \right ) dx</math>.

As for contents of other dimensions, the area of a [[flat]] surface can be calculated by taking the [[double integral]] across the appropriate dimensions—often, appropriately, called an [[area integral]]. In [[Cartesian coordinates]], this simply means <math>A = \iint\;dx\;dy</math>; in [[polar coordinates]] it becomes <math>A = \iint\;r\;dr\;d\theta</math>; in [[parabolic coordinates]] <math>A = \iint\;(u^2 + v^2)\;du\;dv</math>; and so on. For a non-flat surface, an area integral can still be used, but determining the [[infinitesimal]] [[area element]] may be less straightforward. If, for example, the surface in question can be expressed in the form <math>z(x,y)</math> (that is, if the ''z''-coordinate can be expressed as a function of the ''x'' and ''y''-coordinates), then the area of the surface is equal to <math>\iint {\sqrt { \left ( \frac{df}{dx} \right )^2 + \left ( \frac{df}{dy} \right)^2 + 1} \; dx\;dy}</math>.

===Limits===
Even these methods may not work in all cases. For [[iteration|iteratively]] defined [[fractal]]s, there may be no straightforward way of calculating the area of the final fractal, but it may be derived as the [[limit]] of the [[sequence]] of the areas at each step. For instance, consider a [[Koch snowflake]], one of the best-known fractals, with a [[width]] of one unit. The iterative process of the snowflake's creation starts with an [[equilateral triangle]] of area <math>\frac{\sqrt{3}}{4}</math>. In the second step, three new triangles are added with 1/3 the edge length of the original triangle, and therefore 1/9 the area... but since there are three of them, the total area added is 1/3 that of the original triangle, making the total area added <math>\frac {1}{3} \left ( \frac{\sqrt{3}}{4} \right ) = \frac{\sqrt {3}}{12}</math>, and the total area <math>\frac{\sqrt{3}}{4} + \frac{\sqrt {3}}{12} = \frac{4 \sqrt{3}}{4} = \frac{\sqrt{3}}{3}</math>. Now, in each step thereafter, four times as many triangles are added than the previous step, but with the area of each triangle only one ninth that of those of the previous step, so the total area added is 4/9 as much as the previous step. The area added in the ''n''th iteration can therefore be expressed as <math>\frac{\sqrt{3}}{12} \left ( \frac{4}{9} \right )^{(n-1)}</math>, and the total area after the ''n''th iteration as <math>\frac {\sqrt{3}}{4} + \sum_{k=1}^n {\frac{\sqrt{3}}{12} \left ( \frac{4}{9} \right )^{(k-1)}} = \frac {\sqrt{3}}{4} + \frac{\sqrt{3}}{12} \sum_{k=0}^{n-1} {\left ( \frac{4}{9} \right )^k}</math>... a [[geometric series]] which [[convergent series|converges]] at the limit to <math>\frac{\sqrt{3}}{4} + \frac{\sqrt{3}}{12} \sum_{k=0}^\infty {\left ( \frac{4}{9} \right )^k} = \frac{\sqrt{3}}{4} + \frac{\sqrt{3}}{12} \frac{9}{5} = \frac{\sqrt{3}}{4} + \frac{3 \sqrt{3}}{20} = \frac{2 \sqrt{3}}{5}</math>.

Note that the area of a fractal need not be a [[infinity|finite]], [[zero|nonzero]] number. For instance, the [[Sierpiński gasket]] is produced by removing at each iteration inner triangles composing 1/4 of the area of the previous step, meaning that at each iteration the area is multipled by 3/4. This makes the area after ''n'' steps the initial area times <math>\left ( \frac{3}{4} \right )^n</math>... which at the limit as <math>n \to \infty</math> goes to [[zero]]... the Sierpiński gasket has a zero area. Meanwhile, while its [[realmspace|three-dimensional]] analogue the [[tetrix]] has a finite and nonzero surface area—indeed, exactly the same as the surface area of the [[regular tetrahedron]] it starts with, since each iteration adds surfaces of the same total area as it removes, thus leaving the surface area unchanged—its [[orthohedron|orthohedral]] cousin the [[Menger sponge]] does not. The surface area of the Menger sponge is a little harder to calculate, but it turns out that after the ''n''th iteration the surface area of a Menger sponge starting with a cube of side length ''s'' is <math>\frac{4 \cdot 8^n + 2 \cdot 20^n}{3^n}</math> which diverges as <math>n \to \infty</math>... the surface area of the Menger sponge is infinite.

The [[fractal dimension]] of a fractal can give some hints about its area. In general, fractals of dimension 2 have finite area; fractals of dimension between 1 and 2 have zero area (and infinite [[perimeter]]); fractals of dimension between 2 and 3 have infinite surface area.

===Others===
There are some cases for which no [[real analysis|analytical]] method of calculating area is known, or perhaps possible. The area of the [[Mandelbrot set]] is one such case: it can certainly be approximated [[numerical analysis|numerically]], but there is (at the time of this writing) no known closed-form expression for its exact value. (There is a known expression for the area of the Mandelbrot set in terms of certain [[coefficient]]s, but there is no known closed form for these coefficients—they can only be calculated [[recursion|recursively]], and rather inefficiently at that—so this doesn't solve the problem.)

==Units==
Typically, area is just measured in [[unit]]s of [[length]] [[square (arithmetic)|square]]d. For example, the standard [[metric system|metric]] unit of area is the square [[meter]] (or the square centimeter in [[cgs]]), though smaller areas may be measurable in square centimeters, square millimeters, and so on, or larger as square kilometers, square terameters, etc. In the [[English system]] area may be measured in square feet, square inches, square yards, square miles, and so forth, as appropriate. Effectively, the [[square (mathematics)|square]] of any unit of length can be a unit of area; one could (but probably wouldn't) measure areas in square [[Wikipedia:parsec|parsec]]s, square [[wikipedia:cubit|cubit]]s, or square [[Wikipedia:smoot|smoot]]s.

There are also some units of area that are defined directly and not as squares of units of length. One such metric unit is the are, defined as one hundred square meters, though to it's probably more familiar in the [[prefix]]ed form of "hectare" (one hundred ares, or ten thousand square meters). An English unit of area still in common use in many places is the [[Wikipedia:acre|acre]], equal to 43,560 square feet. (One quarter of an acre used to be called a rood, but this is nowadays seldom used.) The acre was originally defined as the amount of land a team of oxen can plow in a day... an important enough consideration in earlier days that many other cultures defined units of area similarly.

Some other, lesser known units of area include the following (units with an asterisk are defined in terms of area plowed, like the acre):
* [[Wikipedia:Barn (unit)|Barn]]: A unit used in [[nuclear physics]] defined as 10<sup>-28</sup> square meters (roughly the cross sectional area of a [[uranium]] [[nucleus (atom)|nucleus]])
* [[Wikipedia:Bigha|Bigha]]: A unit of land area used in [[India]] and some neighboring [[nation]]s, its size varying regionally but generally equal to several thousand square meters. One twentieth of a bigha is sometimes a [[Wikipedia:katha (unit)|katha]]. Other (similarly variable) units used in South Asia are the [[kanal (unit)|kanal]] (about 500 square meters), the karm (about three square meters) , the [[keela]] (about 4,000 square meters), the [[marla (unit)|marla]] (about 20 square meters), and the [[sarsahi]] (a little over two square meters).
* [[Wikipedia:Bunder|Bunder]]: A [[Netherlands|Dutch]] and [[Belgium|Belgian]] unit now defined as equal to one hectare.
* [[Wikipedia:Dunam]]*: A unit of area formerly used in the [[Ottoman Empire]], and still used in some areas that used to belong to it. While its former definition varied, it has in modern times been defined as equal to exactly one thousand square meters (one decare).
* [[Wikipedia:Feddan|Feddan (فدّاʆ)]]*: A unit of area used in various Arabic countries, equal to 4,200 square units. A feddan is divided into 24 ''kirats'' (قيراط).
* [[Wikipedia:Hide (unit)|Hide]]: An [[England|English]] unit of area representing the minimum amount of land that can support a household—and which therefore varied by time and region, but was generally about 120 acres.
* [[Wikipedia:Chinese units of measurement#Area|Mǔ (畝/亩)]]: A [[China|Chinese]] unit of area, now defined as 2/3 of a hectare. One thousandth of a mǔ is a ''háo'' (毫); one hundredth is a ''lí'' (釐/厘); one tenth is a ''fēn'' (市分); and ten mǔ are a ''qǐng'' (頃/顷).
* [[Wikipedia:Ngan|Ngaan (งาน)]]: A unit of area commonly used in [[Thailand]], equal to 400 square meters. Four ngaan compose a ''rai''.
* [[Wikipedia:Quinaria|Quinaria]]: A unit of area used in ancient [[Rome]] to measure the cross-sectional area of a pipe, equal to about 4.5 square centimeters.
* [[Wikipedia:Stremma|Stremma (στρέμμα)]]*: A unit of measurement originating in ancient [[Greece]], still used but now standardized to exactly 1,000 square meters.
* [[Wikipedia:Japanese units of measurement#Area|Tsubo (坪)]]: A [[Japan]]ese unit of area defined as the area of two [[Wikipedia:tatami|tatami]] mats, and standardized as equal to about 3.306 meters. An equivalent unit used in [[agriculture]] is a ''bu'' (歩). Various fractions and multiples of the ''tsubo''/''bu'' have their own names: 1/100 of a ''tsubo'' is a ''shaku'' (勺), 1/10 is a ''gŃ'' (合), 1/2 a ''jŃ'' (畳); 30 ''bu'' are a ''se'' (畝), 300 a ''tan'' (段/反), and 3,000 a ''chŃ'' (町/町歩).
[[Category:Contents]]

← Older revision		Revision as of 05:15, 27 September 2015
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	===Formulæ===		===Formulæ===
	There are some [[shape]]s for which the area can be [[calculation\|calculated]] through relatively simple formulæ. The area of a [[circle]] of [[radius]] ''r'' is <math>2 \pi r</math>; the area of an [[ellipse]] of radii ''a'' and ''b'' is simply <math>\pi a b</math> (of which formula the circle formula may be taken as a special case). Even more generally, the area of a [[superellipse]] of radii ''a'' and ''b'' and of [[exponent]] <math>n</math> is equal to <math>4 a b \frac{(\Gamma ( 1 + \frac {1}{n} ) )^2}{\Gamma (1 + \frac {2}{n} ) }</math>.		There are some [[shape]]s for which the area can be [[calculation\|calculated]] through relatively simple formulæ. The area of a [[circle]] of [[radius]] ''r'' is <math>\pi r^2</math>; the area of an [[ellipse]] of radii ''a'' and ''b'' is simply <math>\pi a b</math> (of which formula the circle formula may be taken as a special case). Even more generally, the area of a [[superellipse]] of radii ''a'' and ''b'' and of [[exponent]] <math>n</math> is equal to <math>4 a b \frac{(\Gamma ( 1 + \frac {1}{n} ) )^2}{\Gamma (1 + \frac {2}{n} ) }</math>.

	The area of a [[regular polygon]] of ''n'' sides each of length ''s'' is <math>\frac{1}{4} n s^2 \cot (\frac {\pi}{n})</math>. The area of a [[rectangle]] is just the product of its length and width. As a special case of both formulae, the area of a [[square (geometry)\|square]] of side length ''s'' is <math>s^2</math>. The area of a [[triangle]] is generally given as <math>\frac{1}{2} b h</math>, with ''b'' and ''h'' respectively its base and height, but there are other forms of this formula for other information, such as [[Hero's formula]] when the lengths of the three sides of the triangle are known. The area of an arbitrary polygon, as long the [[coordinate]]s of its [[vertex\|vertices]] are known, can be derived through an [[expression]] sometimes called the [[shoelace formula]].		The area of a [[regular polygon]] of ''n'' sides each of length ''s'' is <math>\frac{1}{4} n s^2 \cot (\frac {\pi}{n})</math>. The area of a [[rectangle]] is just the product of its length and width. As a special case of both formulae, the area of a [[square (geometry)\|square]] of side length ''s'' is <math>s^2</math>. The area of a [[triangle]] is generally given as <math>\frac{1}{2} b h</math>, with ''b'' and ''h'' respectively its base and height, but there are other forms of this formula for other information, such as [[Hero's formula]] when the lengths of the three sides of the triangle are known. The area of an arbitrary polygon, as long the [[coordinate]]s of its [[vertex\|vertices]] are known, can be derived through an [[expression]] sometimes called the [[shoelace formula]].
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	Some other, lesser known units of area include the following (units with an asterisk are defined in terms of area plowed, like the acre):		Some other, lesser known units of area include the following (units with an asterisk are defined in terms of area plowed, like the acre):
	* [[Wikipedia:Barn (unit)\|Barn]]: A unit used in [[nuclear physics]] defined as 10<sup>-28</sup> square meters (roughly the cross sectional area of a [[uranium]] [[nucleus (atom)\|nucleus]])		* [[Wikipedia:Barn (unit)\|Barn]]: A unit used in [[nuclear physics]] defined as 10<sup>-28</sup> square meters (roughly the cross sectional area of a [[uranium]] [[nucleus (atom)\|nucleus]])
	* [[Wikipedia:Bigha\|Bigha]]: A unit of land area used in [[India]] and some neighboring [[nation]]s, its size varying regionally but generally equal to several thousand square meters. One twentieth of a bigha is sometimes a [[Wikipedia:katha (unit)\|katha]]. Other (similarly variable) units used in South Asia are the [[kanal (unit)\|kanal]] (about 500 square meters), the karm (about three square meters) , the [[keela]] (about 4,000 square meters), the [[marla (unit)\|marla]] (about 20 square meters), and the [[sarsahi]] (a little over two square meters).		* [[Wikipedia:Bigha\|Bigha]]: A unit of land area used in [[India]] and some neighboring [[nation]]s, its size varying regionally but generally equal to several thousand square meters. One twentieth of a bigha is sometimes called a ''[[Wikipedia:katha (unit)\|katha]]''. Other (similarly variable) units used in South Asia are the ''[[Wikipedia:kanal (unit)\|kanal]]'' (about 500 square meters), the ''karm'' (about three square meters) , the ''keela'' (about 4,000 square meters), the ''[[Wikipedia:marla (unit)\|marla]]'' (about 20 square meters), and the ''sarsahi'' (a little over two square meters).
	* [[Wikipedia:Bunder\|Bunder]]: A [[Netherlands\|Dutch]] and [[Belgium\|Belgian]] unit now defined as equal to one hectare.		* [[Wikipedia:Bunder\|Bunder]]: A [[Netherlands\|Dutch]] and [[Belgium\|Belgian]] unit now defined as equal to one hectare.
	* [[Wikipedia:Dunam]]*: A unit of area formerly used in the [[Ottoman Empire]], and still used in some areas that used to belong to it. While its former definition varied, it has in modern times been defined as equal to exactly one thousand square meters (one decare).		* [[Wikipedia:Dunam\|Dunam]]*: A unit of area formerly used in the [[Ottoman Empire]], and still used in some areas that used to belong to it. While its former definition varied, it has in modern times been defined as equal to exactly one thousand square meters (one decare).
	* [[Wikipedia:Feddan\|Feddan (فدّاʆ)]]*: A unit of area used in various Arabic countries, equal to 4,200 square units. A feddan is divided into 24 ''kirats'' (قيراط).		* [[Wikipedia:Feddan\|Feddan (فدّاʆ)]]*: A unit of area used in various Arabic countries, equal to 4,200 square units. A feddan is divided into 24 ''kirats'' (قيراط).
	* [[Wikipedia:Hide (unit)\|Hide]]: An [[England\|English]] unit of area representing the minimum amount of land that can support a household—and which therefore varied by time and region, but was generally about 120 acres.		* [[Wikipedia:Hide (unit)\|Hide]]: An [[England\|English]] unit of area representing the minimum amount of land that can support a household—and which therefore varied by time and region, but was generally about 120 acres.
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	* [[Wikipedia:Quinaria\|Quinaria]]: A unit of area used in ancient [[Rome]] to measure the cross-sectional area of a pipe, equal to about 4.5 square centimeters.		* [[Wikipedia:Quinaria\|Quinaria]]: A unit of area used in ancient [[Rome]] to measure the cross-sectional area of a pipe, equal to about 4.5 square centimeters.
	* [[Wikipedia:Stremma\|Stremma (στρέμμα)]]*: A unit of measurement originating in ancient [[Greece]], still used but now standardized to exactly 1,000 square meters.		* [[Wikipedia:Stremma\|Stremma (στρέμμα)]]*: A unit of measurement originating in ancient [[Greece]], still used but now standardized to exactly 1,000 square meters.
	* [[Wikipedia:Japanese units of measurement#Area\|Tsubo (坪)]]: A [[Japan]]ese unit of area defined as the area of two [[Wikipedia:tatami\|tatami]] mats, and standardized as equal to about 3.306 meters. An equivalent unit used in [[agriculture]] is a ''bu'' (歩). Various fractions and multiples of the ''tsubo''/''bu'' have their own names: 1/100 of a ''tsubo'' is a ''shaku'' (勺), 1/10 is a ''gō'' (合), 1/2 a ''jō'' (畳); 30 ''bu'' are a ''se'' (畝), 300 a ''tan'' (段/反), and 3,000 a ''chō'' (町/町歩).		* [[Wikipedia:Japanese units of measurement#Area\|Tsubo (坪)]]: A [[Japan]]ese unit of area defined as the area of two [[Wikipedia:tatami\|tatami]] mats, and standardized as equal to about 3.306 square meters. An equivalent unit used in [[agriculture]] is a ''bu'' (歩). Various fractions and multiples of the ''tsubo''/''bu'' have their own names: 1/100 of a ''tsubo'' is a ''shaku'' (勺), 1/10 is a ''gō'' (合), 1/2 a ''jō'' (畳); 30 ''bu'' are a ''se'' (畝), 300 a ''tan'' (段/反), and 3,000 a ''chō'' (町/町歩).
	[[Category:Contents]]		[[Category:Contents]]