Area
From Wikipilipinas: The Hip 'n Free Philippine Encyclopedia
--63.3.6.2 02:20, 30 March 2007 (UTC)meeh
Area is a physical quantity expressing the size of a part of a surface. The term can also be used in a non-mathematical context to be mean "vicinity".
Surface area is the summation of the areas of the exposed sides of an object.
Contents |
Mathematical usage
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 = 10^{12} square metres
Imperial units, as currently defined from the metre:
- square foot (plural square feet) = 0.09290304 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
Old European area units, still in used in some private matters (e.g. land sale advertisements)
- square fathom (fahomia in some sources) = 3.34450944 square metres
- cadastral moon(acre) = 1600? square fathoms = 5755 square metres {{fact}
traditional Afghan unit
- jirib ≈0.2 hectare; used typically for field and pasture measurement, and less often in real estate trading
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. |
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 (height), respectively. |
Disk* or Circle | <math>a</math> and <math>b</math> are the semi-major and semi-minor axis. | |
Sphere, Circular area | <math>4 \pi r^2 \,</math>, or <math>\pi d^2 \,</math> | <math>r</math> is the radius and <math>d</math> the diameter. |
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 (h + r) \,</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. |
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. |
* A disk is the area enclosed in a circle. Often such area is called cross-sectional area like a round cable cut in half.
See also
- Volume
- Orders of magnitude (area) — A list of areas by size.
- Equi-areal mapping
External links
Original Source
This page was adapted from the English Wikipedia. The original article was at Area. The list of authors can be seen in the page history. As with Wikipedia, WikiPilipinas also allows reuse of content made available under the Creative Commons Attribution-ShareAlike. See full WikiMedia Terms of Use. |