Area of a Rectangle
What is the Area of a Rectangle?
The area of a rectangle is the total space enclosed within its four sides, found by multiplying its length by its width. It's one of the most fundamental area formulas, and the basis for understanding area as "how many unit squares fit inside a shape."
The closely related perimeter formula, P = 2(l + w), measures the total distance around the outside instead — area and perimeter answer different questions and shouldn't be confused.
What Each Variable Means
When to Use It
- Finding the floor space, land area, or surface area of any rectangular region
- Calculating material needed to cover a rectangular surface
- As a building block for the volume of rectangular prisms
Step-by-Step Examples
Example 1: Finding a room's area
Problem: A room is 6 m long and 4 m wide. What is its area?
Both length and width are given.
l = 6 m, w = 4 mMultiply length by width.
A = 6 × 4Example 2: Finding a missing dimension
Problem: A rectangular garden has an area of 48 m² and a width of 6 m. Find its length.
Solve A = l × w for length.
l = A / wDivide the area by the width.
l = 48 / 6Interactive Calculator
Solving for Other Variables
l = A / wSolve for length when area and width are known.Common Mistakes
Mistake: Confusing area with perimeter.
Fix: Area (A = l × w) measures the enclosed space in square units; perimeter (P = 2(l + w)) measures the distance around the outside in linear units — they answer different questions.
Mistake: Mixing units, like length in meters and width in centimeters.
Fix: Convert both dimensions to the same unit before multiplying, or the resulting area will be wrong by whatever conversion factor was missed.
Practice Questions
A rectangle is 12 cm long and 5 cm wide. Find its area.
A rectangle has area 90 cm² and length 15 cm. Find its width.
Hint: Rearrange A = l × w to solve for w.
Frequently Asked Questions
Does it matter which dimension I call length versus width?
No — the area comes out the same either way, since multiplication is commutative (l × w = w × l). "Length" and "width" are just conventional labels for the two dimensions.
How is this related to the area of a square?
A square is a special rectangle where length and width are equal — substituting l = w = s into A = l × w gives A = s², the square area formula.
Related Formulas
Area of a Square
A square's area is its side length squared, since all four sides are equal.
Learn more →Area of a Circle
Calculate the area enclosed by a circle from its radius.
Learn more →Area of a Triangle
Half the base times the perpendicular height — works for any triangle.
Learn more →