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.

The dimension of area is:

$\mathsf L^2$

Thus:

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

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

$\quad (1): \quad$

The area of a square with a side of length one unit is defined to be one square unit.

$\quad (2): \quad$

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.

$\quad (3): \quad$

Equal surfaces have equal areas.