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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

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.

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.
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