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$A=ℓw$

The length is usually defined as the rectangle's longer sides and the width its shorter sides, but this assignment is arbitrary.

Consider a square of unit side length. In this case, by the definition of area, its surface would be a squared unit. Now, for a rectangle of integer length $ℓ,$ and integer width $w,$ it is possible to divide it unit squares.

Since the original rectangle has side length $ℓ,$ and width $w,$ there are exactly $ℓ$ unit squares in each row and there are $w$ rows of unit squares. Therefore, the total number of unit squares is $ℓ×w.$ Hence, the area of a rectangle of side length $ℓ,$ and width $w$ is $A=ℓw.$ This result is still valid if $ℓ$ and $w$ were any real numbers.