Area

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--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 = 1012 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

Common equations for area:
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

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