Area of a Rectangle — Formula & Worked Examples

The area of a rectangle is the amount of flat space inside it, found by multiplying length by width:

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

Why length times width works

Picture the rectangle 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. The multiplication is not an arbitrary rule; it is literally a count of the squares inside.

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

Start with the formula:

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

Multiply:

So the area is:

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

Try it yourself, then check the answer

Compute the area of a rectangle with length $12$ m and width $7$ m using $A = lw$. You should get $84\ \text{m}^2$. For a second case, try $l = 9$ cm and $w = 9$ cm; the area is $81\ \text{cm}^2$. Keep the units consistent and confirm your final answer is in square units before moving on.

Calculation traps to watch for

1. Adding instead of multiplying. Adding the side lengths finds perimeter, not area.
2. Mixing units. Using meters for one side and centimeters for the other without converting first gives a wrong result.
3. Plain units instead of square units. Writing cm instead of $\text{cm}^2$ is a units error even when the number is right.
4. Assuming the shape is a rectangle. $A = lw$ only applies once you have confirmed the figure actually is a rectangle.

A quick check that your answer makes sense

If one side doubles and the other stays the same, the area should double. If both sides double, the area should become four times as large. This scaling check catches arithmetic mistakes fast.

Where rectangle area shows up

You need it whenever you measure a flat rectangular surface: floor space, wall coverage, paper size, garden beds, tile layouts. It also appears inside larger geometry problems, since splitting a shape into rectangles and finding each rectangle's area is often the first step.