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Encyclopedia > Area

Area is a quantity expressing the two-dimensional size of a defined part of a surface, typically a region bounded by a closed curve. 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 polyhedron. Image File history File links Mergefrom. ... Area is a quantity expressing the size of a figure in the Euclidean plane or on a 2-dimensional surface. ... Look up area in Wiktionary, the free dictionary. ... Quantity is a kind of property which exists as magnitude or multitude. ... 2-dimensional renderings (ie. ... An open surface with X-, Y-, and Z-contours shown. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... For the game magazine, see Polyhedron (magazine). ...

## Units

Units for measuring surface area include:

Metric
square metre (m²) = SI derived unit
are (a) = 100 square metres (m²)
hectare (ha) = 10,000 square metres (m²)
square kilometre (km²) = 1,000,000 square metres (m²)
square megametre (Mm²) = 1012 square metres (m²)
US & Imperial Units
square foot = 144 square inches = 0.09290304 square metres (m²)
square yard = 9 square feet = 0.83612736 square metres (m²)
square perch = 30.25 square yards = 25.2928526 square metres (m²)
acre = 160 square perches or 4,840 square yards or 43,560 square feet = 4046.8564224 square metres (m²)
square mile = 640 acres = 2.5899881103 square kilometres (km²

See: International System of Units, colloquially called the Metric System, and also metrication. ... A square metre (US spelling: square meter) is by definition the area enclosed by a square with sides each 1 metre long. ... SI derived units are part of the SI system of measurement units and are derived from the seven SI base units. ... An are (symbol a) is a unit of area, equal to 100 square meters (10 m Ã— 10 m), used for measuring land area. ... A hectare (symbol ha) is a unit of area, equal to 10 000 square metres, commonly used for measuring land area. ... Square kilometre (U.S. spelling: square kilometer), symbol kmÂ², is a decimal multiple of SI unit of surface area square metre, one of the SI derived units. ... Square megametre (symbol Mm2) is an SI unit of surface area. ... This article is about post-1824 imperial units, see also English unit, U.S. customary units or Avoirdupois. ... A square foot is by definition the area enclosed by a square with sides each 1 foot long. ... -1... A sign at the City Hall in MÃ¼nster, Germany suggesting that the bar shown is one Half Prussian Rod A rod is a unit of length, equal to 5. ... This article is about the unit of measurement. ... A square mile is an English unit of area equal to that of a square with sides each 1 statute mile (â‰ˆ1,609 m) in length. ...

## Useful formulas

Common equations for area:
Shape Equation Variables
Square $s^2,!$ s is the length of the side of the square.
Regular triangle $frac{sqrt{3}}{4}s^2,!$ s is the length of one side of the triangle.
Regular hexagon $frac{3sqrt{3}}{2}s^2,!$ 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.
Any regular polygon $frac{P^2/n} {4 cdot tan(pi/n)},!$ P is the Perimeter and n is the number of sides.
Any regular polygon (using degree measure) $frac{P^2/n} {4 cdot tan(180^circ/n)},!$ P is the Perimeter and n is the number of sides.
Rectangle $lw ,!$ l and w are the lengths of the rectangle's sides (length and width).
Parallelogram (in general) $bh,!$ 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 $frac{1}{2}bh ,!$ b and h are the base and altitude (measured perpendicular to the base), respectively.
Triangle $frac{1}{2} a b sin C,!$ a and b are any two sides, and C is the angle between them.
Circle $pi r^2 ,,!$ 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 $frac{1}{2}(a+b)h ,!$ a and b are the parallel sides and h the distance (height) between the parallels.
Total surface area of a Cylinder $2pi r^2+2pi r h ,!$ 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 $frac{1}{2} r^2 theta ,!$ r and θ are the radius and angle (in radians), respectively.
Square to circular area conversion $frac{4}{pi} A,!$ A is the area of the square in square units.
Circular to square area conversion $frac{1}{4} Cpi,!$ C is the area of the circle in circular units.

All of the above calculations show how to find the area of many shapes. Image File history File links Area. ... An equation is a mathematical statement, in symbols, that two things are the same (or equivalent). ... For other uses, see Square. ... A triangle. ... For other uses, see Hexagon (disambiguation). ... For other uses, see Octagon (disambiguation). ... In geometry, the apothem of a regular polygon is a line drawn from the center of the polygon perpendicular to one of its sides. ... In geometry, a rectangle is defined as a quadrilateral where all four of its angles are right angles. ... A parallelogram. ... Two rhombi. ... In mathematics, diagonal has a geometric meaning, and a derived meaning as used in square tables and matrix terminology. ... A triangle. ... This article or section does not adequately cite its references or sources. ... In geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i. ... A triangle. ... Circle illustration This article is about the shape and mathematical concept of circle. ... DIAMETER is a computer networking protocol for AAA (Authentication, Authorization and Accounting). ... For other uses, see Ellipse (disambiguation). ... The semi-major axis of an ellipse In geometry, the term semi-major axis (also semimajor axis) is used to describe the dimensions of ellipses and hyperbolae. ... In geometry, the semi-minor axis (also semiminor axis) applies to ellipses and hyperbolas. ... This article is about the geometric figure. ... A right circular cylinder An elliptic cylinder In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). ... This article is about the geometric object, for other uses see Cone. ... Slant Height of a Right Circular cone is the Distance from any point on the Circle to the Apex of the Cone. ... For other uses, see Sphere (disambiguation). ... This article is about the shape. ... A circular sector or circle sector also known as a pie piece is the portion of a circle enclosed by two radii and an arc. ... In mathematics and physics, the radian is a unit of angle measure. ... For other uses, see Square. ... For other uses, see Square. ... Circle illustration This article is about the shape and mathematical concept of circle. ... Circle illustration This article is about the shape and mathematical concept of circle. ... In geometry, two sets of points are of the same shape precisely if one can be transformed to another by dilating (i. ...

## See also

This article is about the concept of integrals in calculus. ... Categories: Orders of magnitude (area) ... The 2 x 2 real matrices are the linear mappings of the Cartesian coordinate system into itself by the rule The set of all such real matrices is denoted by M(2,R). ... For other uses, see Volume (disambiguation). ...

Results from FactBites:

 Area of a Circle (332 words) The area of a circle is the number of square units inside that circle. The area of a circle is 78.5 square meters. The area of a coin is 3.14 square centimeters.
 Area (330 words) To determine the lift and drag that a wing generates, you must be able to calculate the area of any of these shapes. The area is the two-dimensional amount of space that an object occupies. Area is measured along the surface of an object and has dimensions of length squared; for example, square feet of material, or centimeters squared.
More results at FactBites »

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