Area of a Rectangle — Formula & Worked Examples

The area of a rectangle is the amount of space inside the shape. To find it, multiply the rectangle's length by its width:

$$A = lw$$

Here, $A$ is area, $l$ is length, and $w$ is width. This works only when both measurements are written in the same unit. The final answer should be in square units such as $\text{cm}^2$, $\text{m}^2$, or $\text{ft}^2$.

Why the formula is length times width

Think of a rectangle as being covered by unit squares. The length tells you how many squares fit across, and the width tells you how many rows of squares fit down.

Multiplying $l$ by $w$ counts all of those squares at once. For example, a rectangle that is $4$ units by $3$ units holds $4 \times 3 = 12$ unit squares, so its area is $12$ square units.

Worked example: a rectangle that is $8$ cm by $5$ cm

Suppose a rectangle has length $8$ cm and width $5$ cm. Start with the formula:

$$A = lw$$

Substitute $l = 8$ and $w = 5$:

$$A = 8 \times 5$$

Multiply:

$$A = 40$$

So the area is:

$$A = 40\ \text{cm}^2$$

The unit is square centimeters, not centimeters, because area measures surface covered rather than distance along an edge.

Common mistakes when finding rectangle area

1. Adding the side lengths instead of multiplying them. That finds perimeter, not area.
2. Mixing units, such as meters for one side and centimeters for the other, without converting first.
3. Writing the result in plain units like cm instead of square units like $\text{cm}^2$.
4. Using $A = lw$ without checking that the shape is actually a rectangle.

When the area of a rectangle formula is used

You use rectangle area whenever you need the size of a flat rectangular surface. Typical examples include floor space, wall coverage, paper size, garden beds, and tile layouts.

It also shows up inside larger geometry problems. If a shape can be split into rectangles, finding the area of each rectangle is often the first step.

A quick check that your answer makes sense

If one side doubles and the other side stays the same, the area should double. If both sides double, the area should become four times as large.

This is a fast way to catch arithmetic mistakes before you move on.

Try a similar problem

Try your own version with length $12$ m and width $7$ m. Use $A = lw$, keep the units consistent, and make sure your final answer is in square meters. If that feels easy, compare it with finding the perimeter of the same rectangle so the two ideas stay separate.