What is the difference between area and perimeter?

Area measures the flat space inside a shape and uses square units, while perimeter measures the distance around the outside and uses linear units. For a rectangle, area uses multiplication (A = \ell \times w), and perimeter uses addition (P = 2\ell + 2w).

Do I multiply or add to find the area of a rectangle?

Always multiply the length and width together. If you add the dimensions, you get something related to perimeter, not area. The key is multiplication.

Why is area measured in square units?

Because area measures flat space in two directions (length and width), the units also go in two directions. When you multiply a measurement in inches by another measurement in inches, you get square inches, which represents area.

Can I use the rectangle area formula for a square?

Yes! A square is a special type of rectangle where all sides are equal in length. You can use A = \ell \times w, or since both sides are the same, you can write A = s^2 where s is the side length.

Area of a Rectangle

Multiply the length and width of a rectangle to find the total area of flat space it covers, measured in square units.

A = \ell w

Solve a problem with Area of a Rectangle

Type the problem. The solver will use Area of a Rectangle where Area of a Rectangle is the right tool, and tell you when it is not.

What each symbol means

What Area of a Rectangle takes

Symbol	Meaning
$A$	The area of the rectangle, which measures the total flat space inside it, expressed in square units like square meters or square centimeters.
$\ell$	The length of the rectangle, representing how far it stretches in one direction, measured in linear units such as meters or feet.
$w$	The width of the rectangle, representing how far it stretches in the perpendicular direction, measured in linear units such as meters or feet.

When to use it

Use this formula when you need to find how much space a rectangle covers.

Level

Usually taught in: Elementary

Worked examples

1. Find the area with whole numbers

Problem

Find the area of a rectangle with length 6 cm and width 4 cm.

$A = \ell w$
Write the area formula for a rectangle.
$A = 6 \times 4$
Substitute $\ell = 6$ cm and $w = 4$ cm into the formula.
$A = 24$
Multiply $6 \times 4 = 24$ .

Answer: $A = 24 \text{ cm}^2$

This example uses simple whole numbers so you can focus on the formula itself. We substitute the values directly and multiply to get 24 square centimeters.

2. Find the area with decimal dimensions

Problem

Find the area of a rectangle with length 7.5 meters and width 6 meters.

$A = \ell w$
Write the area formula.
$A = 7.5 \times 6$
Substitute $\ell = 7.5$ m and $w = 6$ m into the formula.
$A = 45$
Multiply $7.5 \times 6 = 45$ .

Answer: $A = 45 \text{ m}^2$

Decimals work the same way as whole numbers in the area formula—just multiply them as normal and include square units in your answer.

3. Find floor space for a coffee shop renovation

Problem

A coffee shop is renovating its main seating area, which measures 12 feet long and 8 feet wide. How much floor space do they have to work with?

$A = \ell w$
Write the area formula.
$A = 12 \times 8$
Identify that $\ell = 12$ feet and $w = 8$ feet from the problem, then substitute into the formula.
$A = 96$
Calculate $12 \times 8 = 96$ .

Answer: $A = 96 \text{ square feet}$

In word problems, you need to identify which measurements are the length and width from the context, apply the formula, and always express your answer in square units.

Common mistakes

Where Area of a Rectangle usually goes wrong

The mistake	Why it is wrong	The fix
Computing $A = \ell + w$ instead of $A = \ell \times w$	Adding the dimensions gives you a linear measurement related to perimeter, not area.	Area always requires multiplication: multiply the length by the width. If you added them, you found something related to perimeter, not area.
Writing the answer as just a number without square units, like $A = 24$ inches instead of $A = 24$ square inches.	Area is always measured in square units because it represents space in two dimensions, not one.	Always include square units (like square inches, square meters, or $\text{cm}^2$ ) to show that you measured a flat space, not a line.
Using the rectangle area formula for a parallelogram with slanted sides.	Parallelograms require the formula $A = \text{base} \times \text{height}$ because their sides are slanted, not perpendicular.	Use $A = \ell \times w$ only for rectangles and squares. For parallelograms and other shapes, check if you need a different formula.

Tips and when to use something else

A square is a special rectangle where all four sides are equal, so you can use $A = s^2$ where $s$ is the side length.
If you know the area and one dimension, you can find the other dimension by dividing: $\text{width} = \text{area} \div \text{length}$ .
To find the area of an L-shaped room or complex shape, break it into smaller rectangles, find the area of each piece, and add them together.
Don't confuse area with perimeter—area measures the space inside ( $A = \ell \times w$ ), while perimeter measures the distance around the outside ( $P = 2\ell + 2w$ ).

Related formulas

Area of a TriangleCalculates the area enclosed by a triangle given its base and perpendicular height; essential for geometry, SAT, and ACT math problems involving triangles.Area of a ParallelogramFind the area of any parallelogram by multiplying its base by the perpendicular height—a formula that works even when sides aren't perpendicular.Volume of a Rectangular PrismCalculates the space inside a rectangular box by multiplying length, width, and height; essential for storage, shipping, and construction problems.

Frequently asked questions

What is the difference between area and perimeter?: Area measures the flat space inside a shape and uses square units, while perimeter measures the distance around the outside and uses linear units. For a rectangle, area uses multiplication ( $A = \ell \times w$ ), and perimeter uses addition ( $P = 2\ell + 2w$ ).
Do I multiply or add to find the area of a rectangle?: Always multiply the length and width together. If you add the dimensions, you get something related to perimeter, not area. The key is multiplication.
Why is area measured in square units?: Because area measures flat space in two directions (length and width), the units also go in two directions. When you multiply a measurement in inches by another measurement in inches, you get square inches, which represents area.
Can I use the rectangle area formula for a square?: Yes! A square is a special type of rectangle where all sides are equal in length. You can use $A = \ell \times w$ , or since both sides are the same, you can write $A = s^2$ where $s$ is the side length.

Need a different method?

The full solver is not scoped to one formula — type any problem and it will pick the method.

Open the math solver

Reviewed 2026-09-18