Area

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Area

Area is a quantityQuantity

Quantity is a kind of property which exists as magnitude or multitude....
expressing the two-dimensionDimension

In common usage, a dimension is a parameter or measurement required to define the characteristics of an object—i.e....
al size of a defined part of a surfaceSurface

In mathematics, specifically in topology, a surface is a two-dimensional manifold....
, typically a region bounded by a closed curveCurve

In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and con...
. 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 polyhedronPolyhedron

A polyhedron is a geometric shape which in mathematics is defined by three related meanings....
.

Units

Units for measuring surface area include:

MetricMetric

Metric may refer to* Metric system, a system of units developed in France in the 18th century...

square metreSquare metre

The square meter is the SI derived unit of area, with symbol m²....
(m²) = SI derived unitSI derived unit

SI derived units are part of the SI system of measurement units and are derived from the seven SI base units....

areAre

An are is a unit of area, equal to 100 square meters , used for measuring land area....
(a) = 100 square metres (m²)
hectareHectare

A hectare is a unit of area, equal to 10,000 square metres, commonly used for measuring land area....
(ha) = 10,000 square metres (m²)
square kilometreFacts About Square kilometre

Square kilometre, symbol km, is an SI unit of surface area....
(km²) = 1,000,000 square metres (m²)
square megametre (Mm²) = 10¹² square metres
square footSquare foot

The square foot is an Imperial unit / U.S....
= 144 square inches = 0.09290304 square metres (m²)
square yardSquare yard

The square yard is an Imperial unit/U.S....
= 9 square feet = 0.83612736 square metres (m²)
square perch = 30.25 square yards = 25.2928526 square metres (m²)
acreAcre

An acre is the name of a unit of area in a number of different systems, including Imperial units, and United States customar...
= 10 square chains or 160 square perches or 4,840 square yards or 43,560 square feet = 4046.8564224 square metres (m²)
square mileSquare mile

A square mile is an English unit of area equal to that of a square with sides each 1 statute mile in length....
= 640 acres = 2.5899881103 square kilometres (km²)

Useful formulas

Common equationFacts About Equation

An **equation** is a mathematical statement, in symbols, that two things are the same....
s for area:
Shape	Equation	Variables
SquareSquare (geometry) In plane geometry, a square is a polygon with four equal sides, four right angles, and parallel opposite sides....		is the length of the side of the square.
Regular triangleTriangle A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line seg...		is the length of one side of the triangle.
Regular hexagonHexagon In geometry, a hexagon is a polygon with six edges and six vertices....		is the length of one side of the hexagon.
Regular octagonOctagon In geometry, an octagon is a polygon that has eight sides....		is the length of one side of the octagon.
Any regular polygon		is the apothemApothem An apothem of a geometric figure is the perpendicular line segment, usually from the center, to an edge, or the length there... , or the radius of an inscribed circle in the polygon, and is the perimeter of the polygon.
Any regular polygon		is the Perimeter and is the number of sides.
Any regular polygon (using degree measure)		is the Perimeter and is the number of sides.
RectangleRectangle In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles....		and are the lengths of the rectangle's sides (length and width).
ParallelogramParallelogram A parallelogram is a four-sided plane figure that has two sets of opposite parallel sides.... (in general)		and are the length of the base and the length of the perpendicular height, respectively.
RhombusRhombus In geometry, a rhombus is a quadrilateral in which all of the sides are of equal length, i.e., it is an equilateral quadrang...		and are the lengths of the two diagonals of the rhombus.
TriangleTriangle A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line seg...		and are the baseBase (geometry) The base of any geometric figure is any side that you wish to measure from or, , any face that you wish to measure from.... and altitudeAltitude (triangle) In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to the opposite side or an exte... (measured perpendicular to the base), respectively.
TriangleTriangle A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line seg...		and are any two sides, and is the angle between them.
CircleCircle In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed poi...	or	is the radius and the diameterDiameter n geometry, a diameter of a circle is any straight line segment that passes through the center and whose endpoints are on t... .
EllipseEllipse The search term "Elliptical" redirects to this page; for the exercise machine, see Elliptical trainer....		and are the semi-majorSemi-major axis In geometry, the term semi-major axis is used to describe the dimensions of ellipses and hyperbolae. ... and semi-minorSemi-minor axis In geometry, the semi-minor axis is a line segment associated with most conic sections.... axes, respectively.
TrapezoidTrapezoid A trapezoid or trapezium is a quadrilateral two of whose sides are parallel to each other....		and are the parallel sides and the distance (height) between the parallels.
Total surface area of a CylinderCylinder (geometry) In mathematics, a cylinder is a quadric, i.e....		and are the radius and height, respectively.
Lateral surface area of a cylinder		and are the radius and height, respectively.
Total surface area of a ConeCone (geometry) In common usage and elementary geometry, a cone is a solid object obtained by rotating a right triangle around one of its tw...		and are the radius and slant heightFacts About Slant height The slant height of a right circular cone is the distance from any point on the circle to the apex of the cone.... , respectively.
Lateral surface area of a cone		and are the radius and slant height, respectively.
Total surface area of a Sphere	or	and are the radius and diameter, respectively.
Total surface area of an ellipsoid		See the article.
Circular sectorCircular sector A circular sector or circle sector also known as a pie piece is the portion of a circle enclosed by two radii and an...		and are the radius and angle (in radians), respectively.
SquareSquare (geometry) In plane geometry, a square is a polygon with four equal sides, four right angles, and parallel opposite sides.... to circular area conversion		is the area of the squareSquare (geometry) In plane geometry, a square is a polygon with four equal sides, four right angles, and parallel opposite sides.... in square units.
CircularCircle Summary In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed poi... to square area conversion		is the area of the circleCircle In Euclidean geometry, a circle is the set of all points in a plane at a fixed distance, called the radius, from a fixed poi... in circular units.

All of the above calculations show how to find the area of many shapesShapes

Shapes may refer to:*Shapes, the plural of shape, the form, condition or aspect of something...
.

The area of irregular polygons can be calculated using the "Surveyor's formula".

Area

Units

Useful formulas

See also

External links