Area

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This article is about the physical quantity. For other uses, see Area (disambiguation).

Area is a physical quantity expressing the size of a part of a surface. The term Surface area is the summation of the areas of the exposed sides of an object.

1 Units
2 Useful formulae
3 See also
4 External links

Units

Units for measuring surface area include:

square metre = SI derived unit

are = 100 square

hectare = 10,000 square metres

square kilometre = 1,000,000 square metres

square megametre = 10¹² 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

rectangle that has the length of 12cm and the width of 7cm

Useful formulae

Image:Area.svg

Common equations for area:
Shape	Equation	Variables
Square	<math>s^2\,\!</math>	<math>s</math> is the length of the side of the square.
Regular hexagon	<math>\frac{3 \sqrt{3}}{2}s^2\,\!</math>	<math>s</math> is the length of one side of the hexagon.
Regular octagon	<math>2(1+\sqrt{2})s^2\,\!</math>	<math>s</math> is the length of one side of the octagon.
Perfect Pentagon	<math>2.5w^2\,\!</math>	<math>w</math> is the width of one side when all sides are equal.
Perfect Hexagon	<math>4w^2\,\!</math>	<math>w</math> is the width of one side when all sides are equal.
Perfect Octagon	<math>7w^2\,\!</math>	<math>w</math> is the width of one side when all sides are equal.
Perfect Nonagon	<math>4.5w^2\,\!</math>	<math>w</math> is the width of one side when all sides are equal.
Any regular polygon	<math>\frac{1}{2}a p \,\!</math>	<math>a</math> is the apothem, or the radius of an inscribed circle in the polygon, and <math>p</math> is the perimeter of the polygon.
Any regular polygon	<math>\frac{P^2/n} {4 \cdot tan(\pi/n)}\,\!</math>	<math>P</math> is the Perimeter and <math>n</math> is the number of sides.
Any regular polygon	<math>\frac{P^2/n} {4 \cdot tan(180^\circ/n)}\,\!</math>	<math>P</math> is the Perimeter and <math>n</math> is the number of sides.
Rectangle	<math>l \cdot w \,\!</math>	<math>l</math> and <math>w</math> are the lengths of the rectangle's sides (length and width).
Parallelogram (in general)	<math>b \cdot h\,\!</math>	<math>b</math> and <math>h</math> are the length of the base and the length of the perpendicular height, respectively.
Rhombus	<math>\frac{1}{2}ab</math>	<math>a</math> and <math>b</math> are the lengths of the two diagonals of the rhombus.
Triangle	<math>\frac{1}{2}b \cdot h \,\!</math>	<math>b</math> and <math>h</math> are the base and altitude (height), respectively.
Disk* or Circle	<math>\pi r^2 \,\!</math>	<math>r</math> is the radius.
Circle, Circular area	<math>\pi r^2 \,\!</math>, or <math>\pi d^2/4 \,\!</math>	<math>r</math> is the radius and <math>d</math> the diameter.
Ellipse	<math>\pi ab \,\!</math>	<math>a</math> and <math>b</math> are the semi-major and semi-minor axes, respectively.
Trapezoid	<math>\frac{1}{2}(a+b)h \,\!</math>	<math>a</math> and <math>b</math> are the parallel sides and <math>h</math> the distance (height) between the parallels.
Total surface area of a Cylinder	<math>2\pi r^2+2\pi r h \,\!</math>	<math>r</math> and <math>h</math> are the radius and height, respectively.
Lateral surface area of a cylinder	<math>2 \pi r h \,\!</math>	<math>r</math> and <math>h</math> are the radius and height, respectively.
Total surface area of a Cone	<math>\pi r (l + r) \,\!</math>	<math>r</math> and <math>l</math> are the radius and slant height, respectively.
Lateral surface area of a cone	<math>\pi r l \,\!</math>	<math>r</math> and <math>l</math> are the radius and slant height, respectively.
Total surface area of a Sphere	<math>4\pi r^2\,\!</math> or <math>\pi d^2\,\!</math>	<math>r</math> and <math>d</math> are the radius and diameter, respectively.
Total surface area of an ellipsoid		See the article.
Circular sector	<math>\frac{1}{2} r^2 \theta \,\!</math>	<math>r</math> and <math>\theta</math> are the radius and angle (in radians), respectively.
Square to circular area conversion	<math>\frac{4}{\pi} A\,\!</math>	<math>A</math> is the area of the square in square units.
Circular to square area conversion	<math>\frac{1}{4} C\pi\,\!</math>	<math>C</math> is the area of the circle in circular units.