Area

Area is a quantity expressing the size of a region of space. Surface area refers to the summation of the exposed sides of an object. Area (Cx2) is the derivative of volume (Cx3). Area is the antiderivative of length (Cx1).

Table of contents
1 Units
2 Some formulas
3 Ill-defined areas
4 External Link

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

Old British units, as currently defined from the metre:
square foot (plural feet) - 0.09290304 square meters.
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

The article Orders of magnitude links to lists of objects of comparable surface area.

Some formulas

For a two dimensional object the area and surface area are the same:

  • square or rectangle: l × w (where l is the length and w is the width; in the case of a square, l = w.
  • circle: &pi×r2 (where r is the radius)
  • any regular polygon: P × a / 2 (where P = the length of the perimeter, and a is the length of the apothem of the polygon [the distance from the center of the polygon to the center of one side])
  • a parallelogram: B × h (where the base B is any side, and the height h is the distance between the lines that the sides of length B lie on)
  • a trapezoid: (B + b) × h / 2 (B and b are the lengths of the parallel sides, and h is the distance between the lines on which the parallel sides lie)
  • a triangle: B × h / 2 (where B is any side, and h is the distance from the line on which B lies to the other point of the triangle). Alternatively, Heron's formula can be used: √(s×(s-a)×(s-b)×(s-c)) (where a, b, c are the sides of the triangle, and s = (a + b + c)/2 is half of its perimeter)
  • the area between the graphss of two functions is equal to the integral of one function, f(x), minus the integral of the other function, g(x).

Some basic formulas for calculating surface areas of three dimensional objects are:

  • cube: 6×(s2) , where s is the length of any side
  • rectangular box: 2×((l × w) + (l × h) + (w × h)), where l, w, and h are the length, width, and height of the box
  • sphere: 4×π×(r2) , where &pi is the ratio of circumference to diameter of a circle, 3.14159..., and r is the radius of the sphere
  • cylinder: 2×π×r×(h + r), where r is the radius of the circular base, and h is the height
  • cone: π×r×(r + √(r2 + h2)), where r is the radius of the circular base, and h is the height.

See also

An artist should feel free to add some example diagrams.

Ill-defined areas

If one adopts the axiom of choice, then it is possible to prove that there are some shapes whose area cannot be meaningfully defined; see Lebesgue measure. Such 'shapes' (they cannot a fortiori be simply visualised) enter into Tarski's circle-squaring problem (and, moving to three dimensions, in the Banach-Tarski paradox). The sets involved will not arise in practical matters.

External Link



In the News

Corporate Equity Index
"The Human Rights Campaign Foundation's Corporate Equality Index report, released each fall, provides an in-depth analysis and rating of large U.S. employers and their policies and practices pertinent to gay, lesbian, bisexual and transgender employees, consumers and investors."Includes evaluation of issues such as diversity training, domestic partner benefits, and respectful advertising. Includes reports back to 2002. From the Human Rights Campaign.

Smart Voter
Smart Voter provides nonpartisan voter information on current elections in California. Find polling information, FAQs about candidates and issues, information tailored for new voters, children's resources, and more. Also find extensive information about previous elections, including voter turnout and the number of votes and percentages for each candidate and proposition. Includes some information about Ohio elections. From the League of Women Voters of California.

Insects Develop Resistance To Engineered Crops
Cornell University entomologist Anthony Shelton finds when engineered crops containing just one Bt toxin grow near modified plants with two toxins, insects may more rapidly develop resistance to all the engineered plants. A soil bacterium called Bacillus thuringiensis (Bt), whose genes are inserted into crop plants, such as maize and cotton, creates these toxins that are deadly to insects but harmless to humans.

New Mechanism For Nutrient Uptake Discovered
Biologists at the Carnegie Institution's Department of Plant Biology have discovered a new way that plant cells govern nutrient regulation--neighboring pore-like structures at the cell's surface physically interact to control the uptake of a vital nutrient, nitrogen. It is the first time scientists have found that the interaction of neighboring molecules is essential to this regulation. The discovery has widespread potential -- from understanding human diseases, such as kidney function, to engineering better crops.

Joe Janes, the Internet Public Library’s founding director, discusse
link: http://www.youtube.com/watch?v=sbf9brsPew0

New Marker To Identify Cancer Stem Cells Discovered
Researchers have found a marker that can be used to identify stem cells in breast tumors, suggesting a potential simple test that could help determine the best treatment for breast cancer. The marker corresponds to worse outcomes and could help determine treatments.

New Study Explores The Evolution Of Male Parental Care And Female Mult
A new study by Joe Yuichiro Wakano and Yasuo Ihara in the August 2005 issue of the American Naturalist investigates a game-theoretical model in which females gain a direct benefit by multiple mating from the paternal care they elicit for their offspring. As a result, various combinations of male parental care and female multiple mating evolve.

New Neurons Born In Adult Rat Cortex
Recent evidence suggesting that antidepressants may act by triggering the birth of new neurons in the adult hippocampus, the brain's memory hub, has heightened interest in such adult neurogenesis and raised the question: Could new neurons also be sprouting up in the parts of the adult brain involved in the thinking and mood disturbances of depression and anxiety?

Overweight children may develop back pain and spinal abnormalities
Being overweight as a child could lead to early degeneration in the spine, according to a new study.

Food From Cloned Animals Safe? FDA Says Yes, But Asks Suppliers To Hol
The U.S. Food and Drug Administration (FDA) has issued new documents on the safety of animal cloning. "Based on FDA's analysis of hundreds of peer-reviewed publications and other studies on the health and food composition of clones and their offspring, the draft risk assessment has determined that meat and milk from clones and their offspring are as safe as food we eat every day,"said Stephen F. Sundlof, D.V.M., Ph.D., director of FDA's Center for Veterinary Medicine.




MP3 Music Downloads

Preview songs, Download Free Music,Burn CDs at ITunes.com
iTunes_RGB_9mm

 


Google




InformationQuickFind.com - Find Information Fast

Links | Privacy Policy | News |