Surface area

Surface area is the measure of how much exposed area any two- or three-dimensional object has.

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: π×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)

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 π 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.

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 for more details.

External Link

• Conversion Calculator for Units of AREA (http://www.ex.ac.uk/cimt/dictunit/ccarea.htm)