Area

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.

Mathematical Usage

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]}

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*	$\pi \cdot r^{2}\,$	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	$2\pi rh\,$	$r$ 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	$\pi rl\,$	$r$ and $l$ are the radius and slant height, respectively.
Circular sector	${\frac {1}{2}}r^{2}\theta \,$	$r$ and $\theta$ are the radius and angle (in radians), respectively.

* A disk is the area enclosed in a circle. Often such area is called cross-sectional area like a cable or wire.

External links