Class 6 Mathematics · 8 min read · Published 10 October 2026

Perimeter vs Area for Class 6: Difference, Formulas and Solved Examples

By Dishantra Editorial · Reviewed 10 October 2026

A rectangular garden is 12 metres long and 8 metres wide. If you want to put a fence around it, what should you calculate? If you want to cover it with grass, what should you calculate?

Fence around it → perimeter.
Grass covering it → area.

The same rectangle appears in both questions, but the mathematics is different. Understanding that difference is more useful than memorising two formulas without knowing when to use them.

1. What is perimeter?

Perimeter is the total distance around the boundary of a closed shape. Imagine walking once around the edge of a playground. The total distance you walk is its perimeter.

Another way to recognise perimeter is to imagine a piece of string laid exactly along every outer side of the figure. If the string is straightened, its length is the perimeter. This is why perimeter is measured in ordinary length units such as centimetres or metres.

For any polygon, the general rule is simple: perimeter = the sum of the lengths of all its sides. Rectangle and square formulas are shortcuts that use their side patterns.

For a rectangle 8 cm long and 5 cm wide: P = 2(8 + 5) = 26 cm.

2. What is area?

Area measures the space inside a shape. Imagine covering the same rectangle completely with 1 cm × 1 cm squares. The number of unit squares needed is its area.

For an 8 cm × 5 cm rectangle: A = 8 × 5 = 40 cm².

3. Why does area use square units?

A 4 cm × 3 cm rectangle contains 4 unit squares across and 3 rows: 4 × 3 = 12. Each unit square measures 1 cm × 1 cm = 1 cm². Therefore its area is 12 cm², not 12 cm.

4. How do you know which one a question needs?

Ask: Am I measuring the boundary or the space inside?

Do not rely only on a keyword. A question may say “garden” in both a fencing problem and a grass-covering problem. Read what is being measured: the edge of the garden or the region inside it.

These words are useful clues, but the situation itself should still make sense.

5. Solved example: fencing

A rectangular garden is 15 m long and 9 m wide. How much fencing is required for one complete boundary?

This example also gives a useful reasonableness check. The two long sides already total 30 m and the two short sides total 18 m, so 48 m is consistent with the geometry.

We need the distance around the garden: P = 2(15 + 9) = 48 m.

6. Same garden, different question

If grass must cover the entire garden, we need its area: A = 15 × 9 = 135 m².

Same garden. Same dimensions. Different question. Different measurement.

7. Finding a missing dimension from area

A rectangle has area 60 cm² and length 10 cm. Since A = l × b:

When a missing dimension is asked for, write the relationship before substituting numbers. That makes it clearer why division is used: the total area is being split into equal rows or columns of the known length.

60 = 10 × b → b = 60 ÷ 10 = 6 cm

Check: 10 × 6 = 60 cm².

8. Finding a missing dimension from perimeter

Suppose a rectangle has perimeter 30 cm and length 9 cm:

30 = 2(9 + b) → 15 = 9 + b → b = 6 cm

9. Same perimeter does not mean same area

This matters because perimeter and area measure different properties. Changing the proportions of a rectangle can keep the outside distance unchanged while changing how much space lies inside.

Two shapes can have the same perimeter but different areas. The reverse can also happen: shapes can have the same area but different perimeters.

10. Four common mistakes

• Using length × breadth for fencing even though fencing follows the boundary.
• Writing 40 cm for an area that should be 40 cm².
• Using length + breadth for rectangle perimeter instead of accounting for both pairs of opposite sides.
• Assuming equal perimeter means equal area.

Quick check

A room is 7 m long and 5 m wide. Skirting around the room requires 2(7 + 5) = 24 m. The floor area is 7 × 5 = 35 m². Only the area answer needs square units.

Notice how the units help confirm the choice. Skirting is a length, so metres are appropriate. Floor coverage is two-dimensional, so square metres are required.

The easiest distinction to remember

Do not begin with two formulas. Begin with Perimeter = BORDER and Area = INSIDE. Once you know what is being measured, choosing the formula becomes much easier.