AREA

'Area' is a physical quantity expressing the size of a part of a surface. The term can also be used in a non-mathematical context to be mean "vicinity".
'Surface area' is the summation of the areas of the exposed sides of an object.

Contents

Units

Useful formula

See also

External links

Units

Units for 'measuring surface area' include:
:square metre = SI derived unit
:are = 100 square metres
: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

Useful formula

{| class="prettytable"s
|+ Common equations for area:
! Shape
! Equation
! Variables
|-
|Square
|$s^2,!$
|$s$ is the length of the side of the square.
|-
|Regular hexagon
|
|$s$ 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.
|-
|Perfect Hexagon
|$4w^2,!$
|$w$ is the width of one side when all sides are equal.
|-
|Perfect Octagon
|$7w^2,!$
|$w$ is the width of one side when all sides are equal.
|-
|Any regular polygon
|
|$a$ is the apothem, or the radius of an inscribed circle in the polygon, and $p$ is the perimeter of the polygon.
|-
|Any regular polygon
|
|$P$ is the Perimeter and $n$ is the number of sides.
|-
|Any regular polygon
|
|$P$ 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
|
|$a$ and $b$ are the lengths of the two diagonals of the rhombus.
|-
|Triangle
|
|$b$ and $h$ are the base and altitude (height), respectively.
|-
|Disk
★ or Circle
|$pi\; r^2\; ,!$
|$r$ is the radius.
|-
|Circle, Circular area
|$pi\; r^2\; ,!$, 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
|
|$a$ 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
|
|$r$ and $heta$ are the radius and angle (in radians), respectively.
|-
|Square to circular area conversion
|
|$A$ is the area of the square in square units.
|-
|Circular to square area conversion
|
|$C$ is the area of the circle in circular units.
|}

★ A disk is the area enclosed in a circle. Often such area is called ''cross-sectional or ''circular '' area'' like a round cable cut in half.

See also

★ Volume

★ Orders of magnitude (area) — A list of areas by size.

★ Equi-areal mapping

External links

★ Conversion cable diameter to circle cross-sectional area and vice versa