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 = 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.
This result is still valid if s were any .
