Area3 min read

Area of a Rectangle

A = l × w

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

A
AreaThe total space inside the rectangle, in square units.
l
LengthThe longer dimension of the rectangle.
w
WidthThe shorter dimension of the rectangle.

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
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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?

1
Identify the dimensions

Both length and width are given.

l = 6 m, w = 4 m
2
Apply the formula

Multiply length by width.

A = 6 × 4
Answer: A = 24 m²

Example 2: Finding a missing dimension

Problem: A rectangular garden has an area of 48 m² and a width of 6 m. Find its length.

1
Rearrange the formula

Solve A = l × w for length.

l = A / w
2
Substitute and calculate

Divide the area by the width.

l = 48 / 6
Answer: l = 8 m

Interactive Calculator

Result will appear here

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

  1. A rectangle is 12 cm long and 5 cm wide. Find its area.

  2. 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.