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Rule

$A=s_{2}$

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

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 $s$ into unit squares.

Since the original square has a side length $s,$ there are exactly $s$ rows of unit squares, each containing $s$ squares. This means that the total number of unit squares that make up the square is the product of $s$ and $s.$

$Number of Unit Squares:s×s $

This expression can be written as a power of $s.$
$s×s=s_{2} $

The area of the square $A$ can be found by multiplying the number of unit squares by the area of one unit square, $1.$
$A=s_{2}⋅1=s_{2} $

The formula for the area of a square of side length $s$ has been proven. $A=s_{2}$

This result is still valid if $s$ were any real number.

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