Area

Information about Area

This article is about the physical quantity. For other uses, see Area (disambiguation).

Area is a physical quantity expressing the size of a part of a surface. The term Surface area is the summation of the areas of the exposed sides of an object.

Units

Units for measuring surface area include:

square metre = SI derived unit

are = 100 square

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

rectangle that has the length of 12cm and the width of 7cm

Useful formulae

Common equations for area:
Shape	Equation	Variables
Square	$\text{[math]}$	$\text{[math]}$ is the length of the side of the square.
Regular hexagon	$\text{[math]}$	$\text{[math]}$ is the length of one side of the hexagon.
Regular octagon	$\text{[math]}$	$\text{[math]}$ is the length of one side of the octagon.
Perfect Pentagon	$\text{[math]}$	$\text{[math]}$ is the width of one side when all sides are equal.
Perfect Hexagon	$\text{[math]}$	$\text{[math]}$ is the width of one side when all sides are equal.
Perfect Octagon	$\text{[math]}$	$\text{[math]}$ is the width of one side when all sides are equal.
Perfect Nonagon	$\text{[math]}$	$\text{[math]}$ is the width of one side when all sides are equal.
Any regular polygon	$\text{[math]}$	$\text{[math]}$ is the apothem, or the radius of an inscribed circle in the polygon, and $\text{[math]}$ is the perimeter of the polygon.
Any regular polygon	$\text{[math]}$	$\text{[math]}$ is the Perimeter and $\text{[math]}$ is the number of sides.
Any regular polygon	$\text{[math]}$	$\text{[math]}$ is the Perimeter and $\text{[math]}$ is the number of sides.
Rectangle	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the lengths of the rectangle's sides (length and width).
Parallelogram (in general)	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the length of the base and the length of the perpendicular height, respectively.
Rhombus	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the lengths of the two diagonals of the rhombus.
Triangle	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the base and altitude (height), respectively.
Disk* or Circle	$\text{[math]}$	$\text{[math]}$ is the radius.
Circle, Circular area	$\text{[math]}$ , or $\text{[math]}$	$\text{[math]}$ is the radius and $\text{[math]}$ the diameter.
Ellipse	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the semi-major and semi-minor axes, respectively.
Trapezoid	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the parallel sides and $\text{[math]}$ the distance (height) between the parallels.
Total surface area of a Cylinder	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the radius and height, respectively.
Lateral surface area of a cylinder	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the radius and height, respectively.
Total surface area of a Cone	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the radius and slant height, respectively.
Lateral surface area of a cone	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the radius and slant height, respectively.
Total surface area of a Sphere	$\text{[math]}$ or $\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the radius and diameter, respectively.
Total surface area of an ellipsoid		See the article.
Circular sector	$\text{[math]}$	$\text{[math]}$ and $\text{[math]}$ are the radius and angle (in radians), respectively.
Square to circular area conversion	$\text{[math]}$	$\text{[math]}$ is the area of the square in square units.
Circular to square area conversion	$\text{[math]}$	$\text{[math]}$ 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!

External links

Area, adjective areal, from Latin area, adj. arealis, "a piece of level ground, an open space, threshing floor", English from 1538.

area - units of measurement
area (geometry) - the Euclidian geometrical concept
area (subnational entity)

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Quantity is a kind of property which exists as magnitude or multitude. It is among the basic classes of things along with quality, substance, change, and relation. Quantity was first introduced as quantum, an entity having quantity.
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surface is a two-dimensional manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space, E³.
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object is a thing, an entity, or a being. This may be taken in several senses.

In its weakest sense, the word object is the most all-purpose of nouns, and can replace a noun in any sentence at all.
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square metre (also spelled meter, see spelling differences) is the SI derived unit of area, with symbol m². It is defined as the area of a square whose sides measure exactly one metre.
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SI derived units are part of the SI system of measurement units and are derived from the seven SI base units.

Dimensionless derived units

The following SI units are actually dimensionless ratios, formed by dividing two identical SI units.
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An are is a unit of area.

Are or ARE may also refer to:

Åre Municipality, a municipality in Sweden
Åre (ski area) in Sweden
Are language, a language from Papua New Guinea
Are languages, a subgroup of the Are-Taupota languages
A.R.E.

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A hectare (symbol ha, pronounced /ˌhɛkˈtɛə(ɹ)/) is a unit of area equal to 10,000 square metres, or one square hectometre, and commonly used for measuring land area.
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Square kilometre (U.S. spelling: square kilometer), symbol km², is a decimal multiple of the SI unit of surface area, the square metre, one of the SI derived units. 1 km² is equal to:

1,000,000 m²
100 ha (hectare)

Conversely:

1 m² = 0.

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The square yard is an imperial/US customary (non-metric) unit of area, formerly used in most of the English-speaking world but now generally replaced by the square metre outside of the US.
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1 rod =
SI units
0 m 0 cm
US customary / Imperial units
0 ft 0 yd

The rod is a unit of length, equal to 5.5 yards, 11 cubits, 5.0292 metres, 16.
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acre is a unit of area in a number of different systems, including the imperial and US customary systems. The most commonly used acres today are the international acre and, in the United States, the survey acre.

One acre comprises 4,840 square yards or 43,560 square feet.
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square mile is an imperial and US unit of area equal the area of a square of one statute mile. It should not be confused with the archaic miles square, which refers to the number of miles on each side squared.
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equation is a mathematical statement, in symbols, that two things are the same (or equivalent). Equations are written with an equal sign, as in

The equation above is an example of an equality: a proposition which states that two constants are equal.
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In plane (Euclidean) geometry, a square is circle with four sides.

Classification

A square is a regular quadrilateral. Likewise it is also a special case of a rhombus, kite, parallelogram, and trapezoid.
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In geometry, a hexagon is a polygon with six edges and six vertices. A regular hexagon has Schläfli symbol .

Regular hexagon

The internal angles of a regular hexagon (one where all sides and all angles are equal) are all 120° and the hexagon has 720 degrees.
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In geometry, an octagon is a polygon that has eight sides. Regular octagon is represented by Schläfli symbol .

Regular octagons

A regular octagon is an octagon whose sides are all the same length and whose internal angles are all the same size.
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The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides.
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rectangle is defined as a quadrilateral where all four of its angles are right angles.

From this definition, it follows that a rectangle has two pairs of parallel sides; that is, a rectangle is a parallelogram.
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In geometry, a parallelogram is a quadrilateral with two sets of parallel sides. The opposite sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are congruent. The three-dimensional counterpart of a parallelogram is a parallelepiped.
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rhombus (or homb; plural rhombi) is a quadrilateral in which all of the sides are of equal length, i.e., it is awith two pairs of equal adjacent sides. The opposite sides of a kite are not parallel unless the kite is also a rhombus.
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diagonal can refer to a line joining two nonadjacent vertices of a polygon or polyhedron, or in contexts any upward or downward sloping line. The word "diagonal" was originally from the Greek διαγωνιος (diagonios
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A triangle is one of the basic shapes of geometry: a polygon with three corners or and three sides or edges which are straight line segments.

In Euclidean geometry any three non-collinear points determine a triangle and a unique plane, i.e.
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The base of any geometric figure is (for polygons) any side that you wish to measure from or (for polyhedra) any face that you wish to measure (or measure from). Bases are most commonly used in geometric formulae for area and volume.
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In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i.e. forming a right angle with) the opposite side or an extension of the opposite side.
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In geometry, a disk (also spelt disc) is the region in a plane bounded by a circle.

A disk is said to be closed or open according to whether or not it contains the circle that constitutes its boundary.
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circle is the set of all points in a plane at a fixed distance, called the radius, from a given point, the centre.

Circles are simple closed curves which divide the plane into an interior and exterior.
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In classical geometry, a radius (plural: radii) of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment. The radius is half the diameter.
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diameter (Greek words diairo = divide and metro = measure) of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circle. The diameters are the longest chords of the circle.
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ellipse (from the Greek ἔλλειψις, literally absence) is the locus of points on a plane where the sum of the distances from any point on the curve to two fixed points is constant.
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Area

Information about Area

Units

Useful formulae

See also

External links

Dimensionless derived units

Classification

Regular hexagon

Regular octagons