Chapter focus: Perimeter measures the distance around a closed figure, while area measures the surface covered by it. Students learn to distinguish the two ideas and use appropriate units and formulas.

🎯 Learning Goals

• Understand perimeter and area.
• Measure and calculate lengths correctly.
• Use perimeter formulas for rectangles and squares.
• Use area formulas for rectangles and squares.
• Choose appropriate units for length, perimeter and area.
• Solve real-life measurement problems.

📏 1. Perimeter

The perimeter of a closed figure is the total distance around its boundary.

For a rectangle with length l and breadth b:

Perimeter = 2 × (l + b)

For a square with side s:

Perimeter = 4 × s

🟦 2. Area

The area of a plane figure is the amount of surface enclosed by its boundary.

For a rectangle:

Area = length × breadth

For a square:

Area = side × side

📐 3. Units and Conversions

Length uses linear units. Area uses square units.

Be careful not to mix units in a calculation. Convert measurements to compatible units first.

🔍 4. Perimeter vs Area

📋 Worked Examples

Example 1 – Rectangle Perimeter

A rectangle is 12 cm long and 5 cm wide.

Perimeter = 2(12+5) = 34 cm.

Example 2 – Rectangle Area

For the same rectangle, Area = 12×5 = 60 cm².

Example 3 – Square

A square has side 7 m.

Perimeter = 4×7 = 28 m.

Area = 7×7 = 49 m².

Example 4 – Missing Side

A rectangle has perimeter 30 cm and length 10 cm. Since 2(l+b)=30, l+b=15. Therefore b = 15−10 = 5 cm.

🧠 Measurement Reasoning

1. Why is area written in square units but perimeter in ordinary length units?
2. Can two different shapes have the same perimeter but different areas? Explain.
3. Can two different shapes have the same area but different perimeters?
4. Why must units be consistent before applying a formula?
5. Which measure would you use to decide how much fencing is needed around a garden?

📝 Important Practice Questions

1. Define perimeter and area.
2. Write the perimeter formula for a rectangle.
3. Write the area formula for a rectangle.
4. Write both formulas for a square.
5. Find the perimeter of a rectangle 15 cm by 8 cm.
6. Find the area of a rectangle 15 cm by 8 cm.
7. Find the perimeter and area of a square of side 9 cm.
8. A rectangle has length 20 m and breadth 7 m. Find its perimeter.
9. A square has perimeter 36 cm. Find its side.
10. Explain the difference between cm and cm².

🔥 Competency / HOTS Questions

1. A rectangular garden is 18 m by 10 m. A fence is required around it. Should you calculate area or perimeter? Explain.
2. Two rectangles have the same area of 24 cm²: 6×4 and 8×3. Do they have the same perimeter? Calculate.
3. A square and a rectangle have the same perimeter. Can their areas be different? Use an example.
4. A student calculates the area of a 10 cm by 4 cm rectangle as 28 cm². Identify and correct the error.
5. A 1 m square is divided into 100 equal 1 cm × 1 cm squares. What does this show about 1 m²?

🧩 MCQ Practice

1. Perimeter measures — A. surface inside B. distance around C. volume D. mass
2. Area of a rectangle 8 cm × 5 cm is — A. 13 cm² B. 26 cm² C. 40 cm² D. 80 cm²
3. Perimeter of a square of side 6 cm is — A. 12 cm B. 24 cm C. 36 cm D. 18 cm
4. Area is measured in — A. cm B. m C. cm² D. km
5. Perimeter of a rectangle 10 cm by 4 cm is — A. 14 cm B. 20 cm C. 28 cm D. 40 cm
6. Area of a square of side 9 cm is — A. 18 cm² B. 36 cm² C. 81 cm² D. 90 cm²
7. Which is suitable for fencing a field? A. area B. perimeter C. volume D. mass
8. Which statement is correct? A. Area uses linear units B. Perimeter uses square units C. Area uses square units D. Both always use cm²

Answer Key: 1-B, 2-C, 3-B, 4-C, 5-C, 6-C, 7-B, 8-C

📄 Printable Worksheet

1. Find the perimeter of a rectangle 18 cm by 7 cm.
2. Find its area.
3. Find the perimeter and area of a square with side 11 cm.
4. A rectangle has perimeter 40 cm and length 12 cm. Find its breadth.
5. A square has area 64 cm². Find its side.
6. Choose perimeter or area for fencing a playground.
7. Choose perimeter or area for covering a floor with tiles.
8. Explain why area is expressed in square units.
9. Draw a rectangle and label its length and breadth.
10. Create one real-life problem involving perimeter and solve it.

🔁 Quick Revision Table

✅ Chapter Mastery Checklist

• ☐ I can explain perimeter and area.
• ☐ I can choose the correct measure for a problem.
• ☐ I can calculate rectangle perimeter and area.
• ☐ I can calculate square perimeter and area.
• ☐ I use correct units.
• ☐ I can solve missing-side problems.
• ☐ I can apply measurement to real situations.

🔗 Continue Learning

← Back to Class 6 Mathematics Chapter Hub

Continue to Chapter 7 – Fractions →

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