Area of a Rectangle

Consider the unit square, a square with side lengths of one unit. By the definition of area, the space inside the unit square is one square unit. Now, divide a rectangle of some integer length l and some other integer width w into unit squares.

Since the original rectangle has a side length l and a width w, there are exactly w rows of unit squares, each containing l squares. This means that the total number of unit squares that make up the rectangle is the product of l and w. Number of Unit Squares: l * w The area of the rectangle A can be found by multiplying the number of unit squares by the area of one unit square, 1. A=(l * w) * 1=l w The formula for the area of a rectangle of side length l and width w has been proven.

Note that this result is still valid if l and w were any real numbers.