Axiom:Area Axioms

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


 * $(1) \quad$ The area of a square with a side of length one unit is defined to be one square unit.


 * $(2) \quad$ Let a surface be divided into a finite number of smaller non-overlapping surfaces.
 * Let 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.


 * $(3) \quad$ Equal surfaces have equal areas.