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Rule

Area of a Square

The area of a square equals its side length

s

squared.

$A = s^{2}$

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

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

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 \times s

This expression can be written as a power of

s .

s \times 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} \cdot 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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Proof