Area
From Wikipedia, the free encyclopedia
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.
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[edit] Units
Units for measuring surface area include:
- square metre = SI derived unit
- are = 100 square metres
- 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
[edit] Useful formulae
| Shape | Equation | Variables |
|---|---|---|
| Square | <math>s^2\,\!</math> | <math>s</math> is the length of the side of the square. |
| Regular hexagon | <math>\frac{3 \sqrt{3}}{2}s^2\,\!</math> | <math>s</math> is the length of one side of the hexagon. |
| Regular octagon | <math>2(1+\sqrt{2})s^2\,\!</math> | <math>s</math> is the length of one side of the octagon. |
| Any regular polygon | <math>\frac{1}{2}a p \,\!</math> | <math>a</math> is the apothem, or the radius of an inscribed circle in the polygon, and <math>p</math> is the perimeter of the polygon. |
| Any regular polygon | <math>\frac{P^2/n} {4 \cdot tan(\pi/n)}\,\!</math> | <math>P</math> is the Perimeter and <math>n</math> is the number of sides. |
| Any regular polygon (using degree measure) | <math>\frac{P^2/n} {4 \cdot tan(180^\circ/n)}\,\!</math> | <math>P</math> is the Perimeter and <math>n</math> is the number of sides. |
| Rectangle | <math>l \cdot w \,\!</math> | <math>l</math> and <math>w</math> are the lengths of the rectangle's sides (length and width). |
| Parallelogram (in general) | <math>b \cdot h\,\!</math> | <math>b</math> and <math>h</math> are the length of the base and the length of the perpendicular height, respectively. |
| Rhombus | <math>\frac{1}{2}ab</math> | <math>a</math> and <math>b</math> are the lengths of the two diagonals of the rhombus. |
| Triangle | <math>\frac{1}{2}b \cdot h \,\!</math> | <math>b</math> and <math>h</math> are the base and altitude (measured perpendicular to the base), respectively. |
| Triangle | <math>\frac{1}{2}\cdot a \cdot b \cdot sinC\,\!</math> | <math>a</math> and <math>b</math> are any two sides, and <math>C</math> is the angle between them. |
| Circle | <math>\pi r^2 \,\!</math>, or <math>\pi d^2/4 \,\!</math> | <math>r</math> is the radius and <math>d</math> the diameter. |
| Ellipse | <math>\pi ab \,\!</math> | <math>a</math> and <math>b</math> are the semi-major and semi-minor axes, respectively. |
| Trapezoid | <math>\frac{1}{2}(a+b)h \,\!</math> | <math>a</math> and <math>b</math> are the parallel sides and <math>h</math> the distance (height) between the parallels. |
| Total surface area of a Cylinder | <math>2\pi r^2+2\pi r h \,\!</math> | <math>r</math> and <math>h</math> are the radius and height, respectively. |
| Lateral surface area of a cylinder | <math>2 \pi r h \,\!</math> | <math>r</math> and <math>h</math> are the radius and height, respectively. |
| Total surface area of a Cone | <math>\pi r (l + r) \,\!</math> | <math>r</math> and <math>l</math> are the radius and slant height, respectively. |
| Lateral surface area of a cone | <math>\pi r l \,\!</math> | <math>r</math> and <math>l</math> are the radius and slant height, respectively. |
| Total surface area of a Sphere | <math>4\pi r^2\,\!</math> or <math>\pi d^2\,\!</math> | <math>r</math> and <math>d</math> are the radius and diameter, respectively. |
| Total surface area of an ellipsoid | See the article. | |
| Circular sector | <math>\frac{1}{2} r^2 \theta \,\!</math> | <math>r</math> and <math>\theta</math> are the radius and angle (in radians), respectively. |
| Square to circular area conversion | <math>\frac{4}{\pi} A\,\!</math> | <math>A</math> is the area of the square in square units. |
| Circular to square area conversion | <math>\frac{1}{4} C\pi\,\!</math> | <math>C</math> is the area of the circle in circular units. |
[edit] See also
- Volume
- Orders of magnitude (area) — A list of areas by size.
- Equi-areal mapping
[edit] External links
Look up Area in
Wiktionary, the free dictionary.
Wiktionary, the free dictionary.
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