# Area

--63.3.6.2 02:20, 30 March 2007 (UTC)meeh

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.

## Mathematical usage

### 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

Imperial units, as currently defined from the metre:

square foot (plural square feet) = 0.09290304 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

Old European area units, still in used in some private matters (e.g. land sale advertisements)

square fathom (fahomia in some sources) = 3.34450944 square metres
cadastral moon(acre) = 1600? square fathoms = 5755 square metres {{fact}

jirib ≈0.2 hectare; used typically for field and pasture measurement, and less often in real estate trading

### Useful formulae

Common equations for area:
Shape Equation Variables
Square $s^2\,$ $s$ is the length of the side of the square.
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 $\frac{1}{2}a p \,$ $a$ is the apothem, or the radius of an inscribed circle in the polygon, and $p$ is the perimeter of the polygon.
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 $\frac{1}{2}ab$ $a$ and $b$ are the lengths of the two diagonals of the rhombus.
Triangle $\frac{1}{2}b \cdot h \,$ $b$ and $h$ are the base and altitude (height), respectively.
Disk* or Circle $a$ and $b$ are the semi-major and semi-minor axis.
Sphere, Circular area $4 \pi r^2 \,$, or $\pi d^2 \,$ $r$ is the radius and $d$ the diameter.
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 $2 \pi r (h + r) \,$ $r$ 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.
Circular sector $\frac{1}{2} r^2 \theta \,$ $r$ and $\theta$ are the radius and angle (in radians), respectively.

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