# 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.

## 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[citation needed]) = 3.34450944 square metres
cadastral moon(acre) = 1600? square fathoms = 5755 square metres [citation needed]

### Useful formula

Common equations for area:
Shape Equation Variables
Rectangle $l \cdot w \,$ $l$ and $w$ are the lengths of the rectangles sides (length and width).
Triangle $\frac{1}{2}b \cdot h \,$ $b$ and $h$ are the base and altitude (height), respectively.
Disk* or Circle $\pi \cdot r^2 \,$ r is the radius.
Ellipse $\pi \cdot a \cdot b \,$ $a$ 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.
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.
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 cable or wire.