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Rule

# Area of a Square

The area of a square equals its side length squared.

This is the result of multiplying the width and length of the square, both of which measure

### Proof

Consider the unit square, a square with side lengths of one unit. By the definition of area, the space inside the square is one square unit. Now, divide a square of some integer side length into unit squares.
Since the original square has a side length there are exactly rows of unit squares, each containing squares. This means that the total number of unit squares that make up the square is the product of and
This expression can be written as a power of
The area of the square can be found by multiplying the number of unit squares by the area of one unit square,
The formula for the area of a square of side length has been proven.

This result is still valid if were any real number.