Area

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area, measure of the size of a surface region, usually expressed in units that are the square of linear units, e.g., square feet or square meters. In elementary geometry, formulas for the areas of the simple plane figures and the surface areas of simple solids are derived from the linear dimensions of these figures. Examples are given in the table entitled Formulas for Various Areas. The areas of irregular figures, plane or solid, can be computed or closely approximated by the use of integral calculus.

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Area

Wikipedia, the free encyclopedia - Cite This Source

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 term surface area refers to the total area of the exposed surface of a 3-dimensional solid, such as the sum of the areas of the exposed sides of a polyhedron.

Units

Units for measuring surface area include:

Metric

square metre (m²) = SI derived unit

are (a) = 100 square metres (m²)

hectare (ha) = 10,000 square metres (m²)

square kilometre (km²) = 1,000,000 square metres (m²)

square megametre (Mm²) = 10¹² square metres (m²)

US & Imperial Units

square foot = 144 square inches = 0.09290304 square metres (m²)

square yard = 9 square feet = 0.83612736 square metres (m²)

square perch = 30.25 square yards = 25.2928526 square metres (m²)

acre = 160 square perches or 4,840 square yards or 43,560 square feet = 4046.8564224 square metres (m²)

square mile = 640 acres = 2.5899881103 square kilometres (km²)

Useful formulas

Common equations for area:

Shape	Equation	Variables
Square	$s^2,!$	$s$ is the length of the side of the square.
Regular triangle	$frac\{sqrt\{3\}\}\{4\}s^2,!$	$s$ is the length of one side of the triangle.
Regular hexagon	$frac\{3sqrt\{3\}\}\{2\}s^2,!$	$s$ 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.
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.
Any regular polygon	$frac\{P^2/n\}\; \{4\; cdot\; tan(pi/n)\},!$	$P$ is the Perimeter and $n$ is the number of sides.
Any regular polygon (using degree measure)	$frac\{P^2/n\}\; \{4\; cdot\; tan(180^circ/n)\},!$	$P$ is the Perimeter and $n$ is the number of sides.
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 (measured perpendicular to the base), respectively.
Triangle	$frac\{1\}\{2\}cdot\; a\; cdot\; b\; cdot\; sinC,!$	$a$ and $b$ are any two sides, and $C$ is the angle between them.
Circle	$pi\; r^2\; ,!$, or $pi\; d^2/4\; ,!$	$r$ is the radius and $d$ the diameter.
Ellipse	$pi\; ab\; ,!$	$a$ and $b$ are the semi-major and semi-minor axes, respectively.
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	$2pi\; r^2+2pi\; r\; h\; ,!$	$r$ 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.
Total surface area of a Sphere	$4pi\; r^2,!$ or $pi\; d^2,!$	$r$ and $d$ are the radius and diameter, respectively.
Total surface area of an ellipsoid		See the article.
Circular sector	$frac\{1\}\{2\}\; r^2\; theta\; ,!$	$r$ and $theta$ 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	$frac\{1\}\{4\}\; Cpi,!$	$C$ is the area of the circle in circular units.

All of the above calculations show how to find the area of many shapes.

See also

• Integral
• Orders of magnitude (area) — A list of areas by size.
• Equi-areal mapping
• Volume

External links

• Conversion cable diameter to circle cross-sectional area and vice versa
• Area formulas

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