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. Area is an important invariant in the differential geometry of surfaces.

Units

Units for measuring area include:

area (a) = 100 square meters (m²)

hectare (ha) = 100 ares (a) = 10000 square meters (m²)

square kilometre (km²) = 100 hectars (ha) = 10000 ares (a) = 1000000 square metres (m²)

square megametre (Mm²) = 10¹² square metres

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

square yard = = 0.83612736 square metres (m²)

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

acre = 10 square chains (also one furlong by one chain); or 160 square perches; or 4840 square yards; or = 4046.8564224 square metres (m²)

square mile = = 2.5899881103 square kilometers (km²)

Formula

}{4}s^2\,\! ||$s$ is the length of one side of the triangle. |- |Regular hexagon |$\backslash frac\{3\backslash sqrt\{3\}\}\{2\}s^2\backslash ,\backslash !$ |$s$ is the length of one side of the hexagon. |- |Regular octagon |$2\backslash left(1+\backslash sqrt\{2\}\backslash right)s^2\backslash ,\backslash !$ |$s$ is the length of one side of the octagon. |- |Any regular polygon |$\backslash frac\{1\}\{2\}a\; p\; \backslash ,\backslash !$ |$a$ is the apothem, or the radius of an inscribed circle in the polygon, and $p$ is the perimeter of the polygon. |- |Any regular polygon |$\backslash frac\{ns^2\}\; \{4\; \backslash cdot\; \backslash tan(\backslash pi/n)\}\backslash ,\backslash !$ |$s$ is the sidelength and $n$ is the number of sides. |- |Any regular polygon (using degree measure) |$\backslash frac\{ns^2\}\; \{4\; \backslash cdot\; \backslash tan(180^\backslash circ/n)\}\backslash ,\backslash !$ |$s$ is the sidelength and $n$ is the number of sides. |- |Rectangle |$lw\; \backslash ,\backslash !$ |$l$ and $w$ are the lengths of the rectangle's sides (length and width). |- |Parallelogram (in general) |$bh\backslash ,\backslash !$ |$b$ and $h$ are the length of the base and the length of the perpendicular height, respectively. |- |Rhombus |$\backslash frac\{1\}\{2\}ab$ |$a$ and $b$ are the lengths of the two diagonals of the rhombus. |- |Triangle |$\backslash frac\{1\}\{2\}bh\; \backslash ,\backslash !$ |$b$ and $h$ are the base and altitude (measured perpendicular to the base), respectively. |- |Triangle |$\backslash frac\{1\}\{2\}\; a\; b\; \backslash sin(C)\backslash ,\backslash !$ |$a$ and $b$ are any two sides, and $C$ is the angle between them. |- |Circle |$\backslash pi\; r^2\backslash \; \backslash text\{or\}\backslash \; \backslash frac\{\backslash pi\; d^2\}\{4\}\; \backslash ,\backslash !$ |$r$ is the radius and $d$ the diameter. |- |Ellipse |$\backslash pi\; ab\; \backslash ,\backslash !$ |$a$ and $b$ are the semi-major and semi-minor axes, respectively. |- |Trapezoid |$\backslash frac\{1\}\{2\}(a+b)h\; \backslash ,\backslash !$ |$a$ and $b$ are the parallel sides and $h$ the distance (height) between the parallels. |- |Total surface area of a Cylinder |$2\backslash pi\; r^2+2\backslash pi\; r\; h\; \backslash ,\backslash !$ |$r$ and $h$ are the radius and height, respectively. |- |Lateral surface area of a cylinder |$2\; \backslash pi\; r\; h\; \backslash ,\backslash !$ |$r$ and $h$ are the radius and height, respectively. |- |Total surface area of a Cone |$\backslash pi\; r\; (l\; +\; r)\; \backslash ,\backslash !$ |$r$ and $l$ are the radius and slant height, respectively. |- |Lateral surface area of a cone |$\backslash pi\; r\; l\; \backslash ,\backslash !$ |$r$ and $l$ are the radius and slant height, respectively. |- |Total surface area of a Sphere |$4\backslash pi\; r^2\backslash \; \backslash text\{or\}\backslash \; \backslash pi\; d^2\backslash ,\backslash !$ |$r$ and $d$ are the radius and diameter, respectively. |- |Total surface area of an ellipsoid |  |See the article. |- |Circular sector |$\backslash frac\{1\}\{2\}\; r^2\; \backslash theta\; \backslash ,\backslash !$ |$r$ and $\backslash theta$ are the radius and angle (in radians), respectively. |- |Square to circular area conversion |$\backslash frac\{4\}\{\backslash pi\}\; A\backslash ,\backslash !$ |$A$ is the area of the square in square units. |- |Circular to square area conversion |$\backslash frac\{1\}\{4\}\; C\backslash pi\backslash ,\backslash !$ |$C$ is the area of the circle in circular units. |}