# Definition:Area

## Definition

Area is the measure of the extent of a surface.

It has $2$ dimensions and is specified in units of length squared.

Hence the term square as a general vague term for a quantity in $2$ dimensions.

### Dimension

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

## Units

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:

$(1) \quad$ 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.