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 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 can be written as a of
s.
s×s=s2
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=s2⋅1=s2
The formula for the area of a square of side length
s has been proven.
This result is still valid if s were any .