Class 5 Maths Chapter 11 Area and its Boundary – Complete Notes

📐 Chapter 11 – Area and its Boundary

Class: 5 (CBSE)
Subject: Mathematics
Main Concepts: Area, Boundary (Perimeter), Square Units, Comparison of Shapes

📘 Introduction

Sometimes two objects look almost the same in size, but we are not sure which one is bigger. To solve such problems, we use two ideas: area and boundary.

✔ Area tells us how much surface is covered.
✔ Boundary (Perimeter) tells us the length around a shape.

🍭 Whose Slice is Bigger?

Parth and Gini bought dried mango slices. Their slices looked different, so they were confused.

To compare sizes, we can:

Cover the shape with small squares
Count the total number of squares

✔ Area Using Square Units

If one square has side $1$ cm, then its area is:

$1 \text{ cm} \times 1 \text{ cm} = 1 \text{ square cm}$

📏 Area of a Rectangle

If a rectangle has:

Length = $l$ cm
Width = $w$ cm

Then area is:

Area = $l \times w$ square cm

📮 Cover with Stamps

Instead of counting one by one, we can multiply.

If one stamp covers $4$ square cm and the rectangle needs $25$ stamps:
Area = $25 \times 4 = 100$ square cm

📐 Boundary (Perimeter)

The boundary of a shape is the distance around it.

✔ Perimeter of a Rectangle

Perimeter = $2(l + w)$

✔ Perimeter of a Square

If side = $s$, then perimeter = $4s$

🏡 Practice Time – Real Life Problems

Arbaz wants to tile his kitchen floor.
Each tile is $10$ cm × $10$ cm.
Kitchen size: $220$ cm × $180$ cm.

Area of kitchen = $220 \times 180 = 39600$ square cm
Area of one tile = $10^2 = 100$ square cm
Number of tiles = $\dfrac{39600}{100} = 396$

🎨 Cards and Designs

Different greeting cards can have:

Same area but different perimeters
Different shapes but equal space

This shows that same area does not mean same boundary.

👖 My Belt is Longest!

When a sheet is cut into thin strips and joined end to end, the belt becomes very long.

Even though the area remains the same, the boundary changes.

🧠 Important Observation

✔ Same area → different boundaries possible
✔ Same boundary → different areas possible

🌾 Share the Land

Nasreena wants to divide her land equally among her three children.

Each person must get:

Equal number of squares
At least one tree

🌍 Big Units of Area

Area can be measured in different units:

Unit	Used For
Square cm	Small objects (card, book)
Square metre	Room, classroom
Square km	City, state

A square of side $1$ km has area = $1 \text{ square km}$

🧩 King’s Story – Area vs Boundary

Cheggu made rectangles using $100$ metres of wire.

Rectangle: $10 \times 40$
Area = $400$ square m

But when he made:

Rectangle: $20 \times 30$
Area = $600$ square m

Finally, a circle gave the maximum area for the same boundary.

✍️ Practice Questions

1) Define area and boundary.

2) Find the area of a rectangle of length $12$ cm and width $5$ cm.

3) Find the perimeter of a square of side $9$ cm.

4) Can two shapes have same area but different boundary? Explain.

5) Which shape gives maximum area for a fixed boundary?

✅ Quick Revision

✔ Area = space covered
✔ Boundary = distance around
✔ Rectangle area = $l \times w$
✔ Square perimeter = $4s$
✔ Same area ≠ same boundary

🎉 Chapter Complete

After studying this chapter, students can confidently calculate area, find boundary, compare shapes, and solve real-life problems.

Class 5 Maths Worksheet – Area and its Boundary

📝 Complete Worksheet – Area and its Boundary

Class: 5 (CBSE)
Chapter: Area and its Boundary
Main Concepts: Area, Boundary (Perimeter), Square Units 🎯

Section A – Multiple Choice Questions (MCQs)

Q1. Area tells us:

(a) Length of a shape

(b) Distance around a shape

(d) Height of a shape

Q2. The boundary of a shape is also called:

(a) Area

(b) Perimeter

(d) Square unit

Q3. Area of a rectangle of length $8$ cm and width $5$ cm is:

(a) $13$ sq cm

(b) $40$ sq cm

(d) $80$ sq cm

Q4. If the side of a square is $6$ cm, its perimeter is:

(a) $12$ cm

(b) $24$ cm

(d) $18$ cm

✔ Q1 → (c) Space covered by a shape
✔ Q2 → (b) Perimeter
✔ Q3 → (b) $40$ sq cm
✔ Q4 → (b) $24$ cm

Section B – Fill in the Blanks

1) Area is measured in __________ units.

2) Boundary is the __________ around a shape.

3) Area of a rectangle = __________ × __________.

4) Perimeter of a square = __________ × side.

✔ square
✔ distance
✔ length, width
✔ $4$

Section C – Very Short Answer Questions

1) What does area mean?

2) What is boundary?

3) Write the unit used to measure area.

✔ Area means the space covered by a shape.
✔ Boundary is the distance around a shape.
✔ Square cm / square m

Section D – Short Answer Questions

Q1. Find the area of a rectangle of length $14$ cm and width $6$ cm.

Q2. Find the perimeter of a square of side $9$ cm.

Q3. Can two shapes have the same area but different boundaries? Explain.

✔ Area = $14 \\times 6 = 84$ sq cm
✔ Perimeter = $4 \\times 9 = 36$ cm
✔ Yes, shapes can cover equal space but have different outlines.

Section E – Long Answer Questions

Q1. A rectangular garden is $20$ m long and $15$ m wide. Find:

Area
Boundary (Perimeter)

Q2. Explain with an example that same boundary can give different areas.

✔ Area = $20 \\times 15 = 300$ sq m
✔ Perimeter = $2(20 + 15) = 70$ m
✔ Example: Rectangles $10 \\times 40$ and $20 \\times 30$ have same boundary but different areas.

Section F – HOTS / Thinking Questions ⭐

Q1. If the side of a square becomes $3$ times, how many times does its area increase?

Q2. Which shape gives the maximum area for a fixed boundary?

✔ Area becomes $3^2 = 9$ times
✔ A circle gives the maximum area.

🎯 Worksheet Complete

✔ Revise formulas daily
✔ Practice grid-based area problems
✔ Understand difference between area & boundary clearly
✔ You are now **exam-ready** ✅