Area

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

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

200px

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 triangle	<math>\frac{\sqrt{3}}{4}s^2\,\!</math>	<math>s</math> is the length of one side of the triangle.
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.
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 (using degree measure)	<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>lw \,\!</math>	<math>l</math> and <math>w</math> are the lengths of the rectangle's sides (length and width).
Parallelogram (in general)	<math>bh\,\!</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}bh \,\!</math>	<math>b</math> and <math>h</math> are the base and altitude (measured perpendicular to the base), respectively.
Triangle	<math>\frac{1}{2} a b \sin C\,\!</math>	<math>a</math> and <math>b</math> are any two sides, and <math>C</math> is the angle between them.
Circle	<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.

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

Look up Area in
Wiktionary, the free dictionary.

• Conversion cable diameter to circle cross-sectional area and vice versa
• Area formulasaf:Oppervlak