Area

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This article explains the meaning of area as a physical quantity. The article area (geometry) is more mathematical. See also area (disambiguation).

Area is a physical quantity expressing the size of a part of a surface. The term can also be used in a non-mathematical context to be mean "vicinity".

Surface area is the summation of the areas of the exposed sides of an object.

1 Mathematical Usage
- 1.1 Units
- 1.2 Useful formulae
2 See also
3 External links

[edit] Mathematical Usage

[edit] 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 = 10¹² square metres

Imperial units, as currently defined from the metre:

square foot (plural square feet) = 0.09290304 square metres

square yard = 9 square feet = 0.83612736 square metres

square 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

Old European area units, still in used in some private matters (e.g. land sale advertisements)

square fathom (fahomia in some sources^{[citation needed]}) = 3.34450944 square metres

cadastral moon(acre) = 1600? square fathoms = 5755 square metres ^{[citation needed]}

[edit] Useful formulae

Common equations for area:
Shape	Equation	Variables
Rectangle	$l \cdot w \,$	$l$ and $w$ are the lengths of the rectangles sides (length and width).
Triangle	$\frac{1}{2}b \cdot h \,$	$b$ and $h$ are the base and altitude (height), respectively.
Disk* or Circle	$\pi \cdot r^2 \,$	r is the radius.
Ellipse	$\pi \cdot a \cdot b \,$	$a$ and $b$ are the semi-major and semi-minor axis.
Sphere, Circular area	$4 \pi r^2 \,$ , or $\pi d^2 \,$	$r$ is the radius and $d$ the diameter.
Trapezoid	$\frac{1}{2}(a+b)h \,$	$a$ and $b$ are the parallel sides and $h$ the distance (height) between the parallels.
Cylinder	$2 \pi r (h + r) \,$	$r$ and $h$ are the radius and height, respectively.
Lateral surface area of a cylinder	$2 \pi r h \,$	$r$ and $h$ are the radius and height, respectively.
Cone	$\pi r (l + r) \,$	$r$ and $l$ are the radius and slant height, respectively.
Lateral surface area of a cone	$\pi r l \,$	$r$ and $l$ are the radius and slant height, respectively.
Circular sector	$\frac{1}{2} r^2 \theta \,$	$r$ and $θ$ are the radius and angle (in radians), respectively.