Surface area
Appearance
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 Imperial 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.
Surface area formulae
Note: For 2D figures, the surface area and the area are the same.
Common equations for surface area (2-Dimensional Objects): | ||
---|---|---|
Shape | Equation | Variables |
A square: | s = length of any side | |
A rectangle: | l = length, w = width | |
A circle: | r = radius | |
Any regular polygon: | P = length of the perimeter, a = length of the apothem of the polygon (the distance from the center of the polygon to the center of one side) | |
A parallelogram: | B (base) = any side, h (height) = the distance between the lines that the sides of length B lie on | |
A trapezoid: | B and b = lengths of the parallel sides, h = distance between the lines on which the parallel sides lie | |
A triangle (1): | B = any side, h = distance from the line on which B lies to the other point of the triangle | |
A triangle (2) | a, b and 'c = sides of triangle, p = half of the perimeter, or (a+b+c)/2
|
Common equations for surface area (3-Dimensional Objects): | ||
---|---|---|
Shape | Equation | Variables |
A cube: | s = length of any side | |
A rectangular prism: | l = length, w = width, h = "h"eight | |
A sphere: | r = radius of sphere | |
A cylinder: | r = radius of circular base, h = height | |
A cone: | r = radius of circular base, "h" = height
|
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.