Definition:Area

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.

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.