# Axiom:Area Axioms

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## Axioms of Area

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

- $(2) \quad$ 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.