Area and Perimeter of a Rectangle: Formula, Examples, and Common Mistakes

Rectangles are everywhere — in the shape of your notebook, your classroom door, a football field, or a phone screen. Because of this, "area and perimeter of a rectangle" is one of the most searched math topics by students all over the world. In this post, you'll learn the formulas, see step-by-step examples, and discover the mistakes students make most often.

What is a Rectangle?

A rectangle is a four-sided shape (quadrilateral) where:

• Opposite sides are equal in length
• All four angles are exactly 90 degrees (right angles)

A rectangle has two dimensions: length (l) and width (w), sometimes called length and breadth.

Area of a Rectangle

The area of a rectangle tells you how much surface it covers. Think of it as how many 1-unit squares would fit inside the shape.

Formula:

Area = length × width

Or simply: A = l × w

Example 1:

A rectangle has a length of 8 cm and a width of 5 cm. Find its area.

• Area = l × w
• Area = 8 × 5
• Area = 40 cm²

Always remember: area is measured in square units (cm², m², ft², etc.) because you're covering a flat surface.

Perimeter of a Rectangle

The perimeter is the total distance around the outside of the rectangle — imagine walking along all four sides and adding up the distance.

Formula:

Perimeter = 2 × (length + width)

Or simply: P = 2(l + w)

Example 2:

Using the same rectangle (length = 8 cm, width = 5 cm), find the perimeter.

• Perimeter = 2 × (l + w)
• Perimeter = 2 × (8 + 5)
• Perimeter = 2 × 13
• Perimeter = 26 cm

Perimeter is measured in regular linear units (cm, m, ft) — not squared, because it's a length, not a surface.

Area vs. Perimeter: What's the Difference?

It's easy to confuse these two, so here's a simple side-by-side comparison:

Area:

• What it measures: the space inside the shape
• Formula: l × w
• Unit: square units (cm², m²)
• Real-life use: flooring, paint, land size

Perimeter:

• What it measures: the distance around the shape
• Formula: 2(l + w)
• Unit: linear units (cm, m)
• Real-life use: fencing, border, framing

In short — area tells you how much space is inside, while perimeter tells you how far it is around the shape.

Common Mistakes Students Make

1. Mixing up area and perimeter formulas. Students often multiply when they should add, or forget the "2 ×" in the perimeter formula.
2. Forgetting the square unit for area. Writing "40 cm" instead of "40 cm²" is a very common error in exams.
3. Using the wrong values. Some students accidentally use two lengths or two widths instead of one of each.
4. Not simplifying units. If length is in meters and width is in centimeters, students forget to convert both to the same unit before calculating.

Practice Problem

Try this one yourself before checking the answer:

A rectangular garden is 12 meters long and 7 meters wide. Find both its area and perimeter.

Click to see the answer

• Area = 12 × 7 = 84 m²
• Perimeter = 2 × (12 + 7) = 2 × 19 = 38 m

Quick Recap

• Area = length × width (measured in square units)
• Perimeter = 2 × (length + width) (measured in linear units)
• Always double-check your units before writing your final answer

Understanding these two formulas is a foundation for more advanced geometry topics like the area and perimeter of squares, triangles, and circles — so make sure you're confident with rectangles first!