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

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	${\frac {3{\sqrt {3}}}{2}}s^{2}\,\!$	$s$ 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.
Any regular polygon	${\frac {1}{2}}ap\,\!$	$a$ 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	$lw\,\!$	$l$ and $w$ are the lengths of the rectangle's sides (length and width).
Parallelogram (in general)	$bh\,\!$	$b$ 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	${\frac {1}{2}}bh\,\!$	$b$ and $h$ are the base and altitude (measured perpendicular to the base), respectively.
Triangle	${\frac {1}{2}}ab\sin C\,\!$	$a$ 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	$2\pi r^{2}+2\pi rh\,\!$	$r$ and $h$ are the radius and height, respectively.
Lateral surface area of a cylinder	$2\pi rh\,\!$	$r$ 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	$\pi rl\,\!$	$r$ and $l$ are the radius and slant height, respectively.
Total surface area of a Sphere	$4\pi r^{2}\,\!$ 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	${\frac {1}{4}}C\pi \,\!$	$C$ is the area of the circle in circular units.