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Area
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This article is about the physical quantity. For other uses, see Area (disambiguation).
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.
Useful formulas
圖片參考:
http://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/Area.svg/200px-Area.svg.png
Common equations for area:
Shape
Equation
Variables
Square
圖片參考:
http://upload.wikimedia.org/math/9/e/f/9efae2c381598cd93b1e4c9a2dd1cd82.png
s is the length of the side of the square.
Regular triangle
圖片參考:
http://upload.wikimedia.org/math/a/f/0/af0f6322f35f2a986ae7376e61885f75.png
s is the length of one side of the triangle.
Regular hexagon
圖片參考:
http://upload.wikimedia.org/math/2/7/d/27d180f80dd0ef22e058da9ab919bf9a.png
s is the length of one side of the hexagon.
Regular octagon
圖片參考:
http://upload.wikimedia.org/math/5/5/b/55befe8b44add8938c4914ffe8e8babe.png
s is the length of one side of the octagon.
Any regular polygon
圖片參考:
http://upload.wikimedia.org/math/1/1/1/11161c479c1bda107ad57c941ca0a633.png
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
圖片參考:
http://upload.wikimedia.org/math/7/e/9/7e9e79240c1bf87c55f90e2bd5324aff.png
P is the Perimeter and n is the number of sides.
Any regular polygon (using degree measure)
圖片參考:
http://upload.wikimedia.org/math/1/d/1/1d1e9343aca923b7bf1f93e5d3e5f0dd.png
P is the Perimeter and n is the number of sides.
Rectangle
圖片參考:
http://upload.wikimedia.org/math/0/b/8/0b85e50acaea901014da7871c8e193f9.png
l and w are the lengths of the rectangle's sides (length and width).
Parallelogram (in general)
圖片參考:
http://upload.wikimedia.org/math/7/1/8/718fdc368f8d614d7a93bc36ae7245d1.png
b and h are the length of the base and the length of the perpendicular height, respectively.
Rhombus
圖片參考:
http://upload.wikimedia.org/math/c/3/8/c38e0e1c4ad81b19979335104d6e267a.png
a and b are the lengths of the two diagonals of the rhombus.
Triangle
圖片參考:
http://upload.wikimedia.org/math/f/6/a/f6a8a4ef1646892407d76f783257099a.png
b and h are the base and altitude (measured perpendicular to the base), respectively.
Triangle
圖片參考:
http://upload.wikimedia.org/math/4/f/e/4fe3fc8bb778880038295c41e57bff95.png
a and b are any two sides, and C is the angle between them.
Circle
圖片參考:
http://upload.wikimedia.org/math/5/a/9/5a9c98e8dda298f710272ed81b88008d.png
r is the radius and d the diameter.
Ellipse
圖片參考:
http://upload.wikimedia.org/math/e/e/c/eec18db3c5fedb7eba42db3557880902.png
a and b are the semi-major and semi-minor axes, respectively.
Trapezoid
圖片參考:
http://upload.wikimedia.org/math/1/b/2/1b2806ec4e2fb163e65f1da175fa00de.png
a and b are the parallel sides and h the distance (height) between the parallels.
Total surface area of a Cylinder
圖片參考:
http://upload.wikimedia.org/math/0/6/2/06297123f345d77ab7e82c8bedfe15e1.png
r and h are the radius and height, respectively.
Lateral surface area of a cylinder
圖片參考:
http://upload.wikimedia.org/math/2/d/9/2d96b91c66569fdb915faeef48cb0aef.png
r and h are the radius and height, respectively.
Total surface area of a Cone
圖片參考:
http://upload.wikimedia.org/math/0/4/6/046012647b8da9f10ff3b4ce6bfb55ff.png
r and l are the radius and slant height, respectively.
Lateral surface area of a cone
圖片參考:
http://upload.wikimedia.org/math/5/e/7/5e7da0b843a577bbc0f22c8d61297952.png
r and l are the radius and slant height, respectively.
Total surface area of a Sphere
圖片參考:
http://upload.wikimedia.org/math/9/d/8/9d862a6169e42e7026ab4831fd7a6868.png
r and d are the radius and diameter, respectively.
Total surface area of an ellipsoid
See the article.
Circular sector
圖片參考:
http://upload.wikimedia.org/math/f/7/a/f7a78fb9bb8282a8caab10e6dec49b9e.png
r and θ are the radius and angle (in radians), respectively.
Square to circular area conversion
圖片參考:
http://upload.wikimedia.org/math/6/a/8/6a80d9aae6792c9afd51f59b9fb51a2d.png
A is the area of the square in square units.
Circular to square area conversion
圖片參考:
http://upload.wikimedia.org/math/7/3/a/73a0bb638708486a13a6db0a32e5779c.png
C is the area of the circle in circular units.