Definition:Area

Definition
Area is the measure of the extent of a surface.

It has two dimensions and is specified in units of length squared.

Hence the term "square" as a general vague term for a quantity in two dimensions.

Dimension
Area is a dimension of measurement of physics.

The dimension of area is $L^2$: length squared.

Units

 * The SI unit of area is the square meter $\mathrm m^2$.
 * The CGS unit of area is the square centimeter $\mathrm {cm}^2$.

Thus:
 * $1 \ \mathrm m^2 = 10^4 \ \mathrm {cm}^2$

Axioms of Area
When discussing areas of surfaces, we usually take the following statements to be axiomatic:


 * 1) The area of a square with a side of length one unit is defined to be one square unit.
 * 2) If we divide a surface into a finite number of smaller non-overlapping surfaces, such that the smaller surfaces cover the entire larger surface, then the sum of the areas of the smaller surfaces equals the area of the larger surface.
 * 3) Equal surfaces have equal areas.