Area

From Wikipedia, the free encyclopedia

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 {{fact}

traditional Afghan unit

jirib ≈0.2 hectare; used typically for field and pasture measurement, and less often in real estate trading

[edit] Useful formulae

Common equations for area:
Shape	Equation	Variables
Square	$s^2\,$	$s$ is the length of the side of the square.
Regular hexagon	$\frac{3 \sqrt{3}}{2}s^2\,$	$s$ is the length of one side of the hexagon.
Regular octagon	$2(1+\sqrt{2})s^2\,$	$s$ is the length of one side of the octagon.
Perfect octagon	$7 w 2$	$w$ is the width of one side when all sides are equal
Any regular polygon	$\frac{1}{2}a p \,$	$a$ is the apothem, or the radius of an inscribed circle in the polygon, and $p$ is the perimeter of the polygon.
Rectangle	$l \cdot w \,$	$l$ and $w$ are the lengths of the rectangle's sides (length and width).
Parallelogram (in general)	$b \cdot h\,$	$b$ and $h$ are the length of the base and the length of the perpendicular height, respectively.
Rhombus	$\frac{1}{2}ab$	$a$ and $b$ are the lengths of the two diagonals of the rhombus.
Triangle	$\frac{1}{2}b \cdot h \,$	$b$ and $h$ are the base and altitude (height), respectively.
Disk* or Circle	$\pi r^2 \,$	$r$ is the radius.
Circle, Circular area	$\pi r^2 \,$ , or $\pi d^2/4 \,$	$r$ 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.
Total surface area of a Cylinder	$2\pi r2+2\pi r h \,$	$r$ 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.
Total surface area of a 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.
Square to circular area conversion	$\frac{4}{\pi} A\,$	$A$ is the area of the square in square units.
Circular to square area conversion	$\frac{1}{4} C\pi\,$	$C$ is the area of the circle in circular units.