Perimeter and Area – Class 5 Explained in the Easiest Way

Key Learning Outcomes

By the end of this chapter, “Perimeter and Area”, readers will:

• Understand the meaning of Perimeter and Area
• Identify and differentiate between Perimeter and Area
• Apply formulas to find the Perimeter and Area of basic shapes
• Use correct units of measurement
• Relate mathematical concepts to real life
• Solve word problems
• Develop problem-solving and visualization skills
• Build practical mathematical understanding

Introduction

Have you ever tried putting a fence around your garden or carpeting your room and wondered how much material you’ll need?
That’s where Perimeter and Area come in!

In simple words,

• Area tells us the space inside a shape (the surface it covers).
• Perimeter tells us the distance around a shape (the boundary).

These two concepts are like best friends in mathematics — they often appear together but have totally different meanings.

Let’s explore these two concepts step by step in a fun and easy way — just like your smart friend explaining maths in class!

What is Perimeter?

Perimeter means the total distance around the boundary of a closed figure.

or

The perimeter is the total length of all sides of a closed shape.

In simpler words, if you walk all the way around the edge of a shape — that distance is its perimeter.

Formula:

For different shapes, the perimeter formula changes a little:

• Rectangle: 2 × (Length + Breadth)
• Square: 4 × Side
• Triangle: Sum of all three sides
• Circle: 2 × π × Radius (but you’ll learn this in higher classes)

Example:

If a rectangle has a length of 8 cm and a breadth of 5 cm,
then,
Perimeter = 2 × (8 + 5) = 26 cm.

That means the total boundary of the rectangle is 26 cm long.

Real-Life Connection:

Imagine you’re putting a fence around your rectangular garden. You need to know the perimeter to buy the right length of fencing wire.

Shape	Formula	Example
Square	4 × side	If side = 5 cm → 4 × 5 = 20 cm
Rectangle	2 × (Length + Breadth)	2 × (8 + 6) = 28 cm
Triangle	Sum of all sides	4 + 5 + 6 = 15 cm
Circle	2πr (Circumference)	If radius = 7 cm → 2 × 3.14 × 7 = 43.96 cm

Takeaway:

1. Perimeter helps us measure how much boundary a shape has.
2. Whenever you need to fence a park, decorate a border, or measure a frame, you are finding its perimeter!

What is Area?

Area is the amount of space covered by a shape or surface.

Imagine spreading a mat on the floor — the total surface it covers is its area.

or

If you spread a mat, lay tiles, or paint a wall — you’re covering an area.

Formula:

For common shapes,

• Circle: π × Radius² (for higher classes)
• Rectangle: Area = Length × Breadth
• Square: Area = Side × Side
• Triangle: (½) × Base × Height

Example:

If a rectangular garden has a length of 8 m and a breadth of 5 m,
Area = Length × Breadth = 8 × 5 = 40 m² (square meters)

That means the garden covers 40 square meters of land.

Real-Life Connection:

When you want to paint a wall or cover your floor with tiles, you need to know its area — not perimeter!

Shape	Formula	Example
Square	Side × Side	If side = 5 cm → 5 × 5 = 25 cm²
Rectangle	Length × Breadth	8 × 6 = 48 cm²
Triangle	½ × Base × Height	½ × 6 × 4 = 12 cm²
Circle	πr²	3.14 × 7 × 7 = 153.86 cm²

Takeaway:

1. Area tells us how much surface a shape covers.
2. Whenever you need to paint a wall, lay tiles, or grow grass, you calculate the area — because you’re covering the surface.

Difference Between Perimeter and Area:

Feature	Perimeter	Area
Meaning	Distance around a shape	Space inside a shape
Measurement Unit	cm, m, km	cm², m², km²
Example	Fencing a park	Covering the park with grass
Formula (Rectangle)	2 × (L + B)	L × B

Finding Perimeter and Area of Common Shapes:

1. Square

A square has all sides equal.

• Perimeter: 4 × Side
• Area: Side × Side

Example:

Side = 6 cm
Perimeter = 4 × 6 = 24 cm
Area = 6 × 6 = 36 cm²

2. Rectangle

A rectangle has opposite sides equal.

• Perimeter: 2 × (Length + Breadth)
• Area: Length × Breadth

Example:

Length = 10 cm, Breadth = 4 cm
Perimeter = 2 × (10 + 4) = 28 cm
Area = 10 × 4 = 40 cm²

3. Triangle

• Perimeter: Sum of all sides
• Area: (½) × Base × Height

Example:

Sides = 3 cm, 4 cm, 5 cm
Perimeter = 3 + 4 + 5 = 12 cm
If base = 4 cm and height = 3 cm,
Area = ½ × 4 × 3 = 6 cm²

Real-Life Uses of Perimeter and Area:

Activity	What You Find	Example
Building a fence	Perimeter	Around your school playground
Laying carpet or tiles	Area	Inside your classroom
Decorating a photo frame	Perimeter	Border length needed
Painting a wall	Area	Surface to paint
Making a garden bed	Both	Fence length and soil area

Quick Recap Formulas:

Shape	Perimeter	Area
Square	4 × side	side × side
Rectangle	2 × (L + B)	L × B
Triangle	a + b + c	½ × base × height
Circle	2πr	πr²

Quick Tips to Remember:

• Perimeter = Outside boundary
• Area = Inside space
• Always use the same units (like cm or m).
• For area, write units as square (cm², m²).
• Practice with real-life objects, such as notebooks, windows, or floors.

Fun Facts

• The unit for area is always written with a square (²) symbol because it covers two dimensions — length and breadth.
• Farmers use area to measure their fields, while architects use perimeter to design boundary walls!

Summary

So, in short:

• Perimeter measures the boundary.
• Area measures the surface inside.
• Both are super useful in our daily life — from decorating a room to planning a park!

Before buying materials like:

• Wire, rope, or border stones → find Perimeter.
• Tiles, paint, or grass → find Area.

This small step can save you time, money, and effort!

If you understand how to use both correctly, you’ll find many real-world problems easy to solve — and math will become one of your favorite subjects!

Practice Questions:

A. Fill In The Blanks.

1. The total distance around a figure is called its ____________.
2. The amount of surface covered by a figure is called its ____________.
3. The area of a rectangle is given by ____________.
4. The perimeter of a square is ____________.
5. The standard unit of area is ____________.

Answers

1. Perimeter
2. Area
3. Length × Breadth
4. 4 × Side
5. Square metre (m²)

B. Match The Following.

Column A	Column B
1. Square	a. 2 × (length + breadth)
2. Rectangle	b. 4 × side
3. Triangle	c. Sum of all sides
4. Circle	d. 2 × π × radius

Answers

1. b
2. a
3. c
4. d

C. Short Answer Questions.

1. What is the difference between perimeter and area?
2. Find the perimeter of a rectangle whose length is 12 m and breadth is 8 m.
3. Find the area of a square whose side is 9 m.
4. The sides of a triangle are 8 cm, 10 cm, and 12 cm. Find its perimeter.
5. A rectangular park is 50 m long and 40 m wide. Find its area.

Answers

1. Difference between Perimeter and Area:
   • Perimeter is the total distance around a shape.
   • Area is the amount of surface a shape covers.
2. Perimeter of rectangle (12 m × 8 m): Perimeter = 2 × (12 + 8) = 40 m
3. Area of square (side 9 m): Area = 9 × 9 = 81 m²
4. Perimeter of triangle (8, 10, 12): Perimeter = 8 + 10 + 12 = 30 cm
5. Area of rectangle (50 m × 40 m): Area = 50 × 40 = 2000 m²

D. Word Problem

1. A farmer wants to fence his square field whose side is 25 m. Find the length of the fence required.
2. The floor of a classroom is 8 m long and 6 m wide. Find the area of the floor and the cost of polishing it at ₹20 per m².
3. A rectangular garden is 30 m long and 20 m wide. Find:
   • (a) Its perimeter
   • (b) Its area
4. A square field has an area of 49 m². Find its perimeter.

Answers

1. Square field fencing:
   Perimeter = 4 × 25 = 100 m
   The farmer needs 100 metres of wire.

2. Classroom floor:
Area = 8 × 6 = 48 m²
Cost = 48 × ₹20 = ₹960
The polishing cost is ₹960.

3. Garden:
(a) Perimeter = 2 × (30 + 20) = 100 m
(b) Area = 30 × 20 = 600 m²

4. Square field (Area = 49 m²):
Side = √49 = 7 m
Perimeter = 4 × 7 = 28 m

E. Higher Thinking Questions

1. Two rectangles have the same perimeter but different areas. Can you draw such examples?
2. Why is the unit of area written as “square units”?
3. Which one changes faster — area or perimeter — when you increase the sides of a shape?

Answers

1. Examples:

• Rectangle 8 m × 2 m → Perimeter = 20 m, Area = 16 m²
• Square 5 m × 5 m → Perimeter = 20 m, Area = 25 m²

2. Reason for square units:
Because area is calculated by multiplying two lengths (length × breadth).

3. Area changes faster when dimensions increase — because it’s based on multiplication, not just addition.

Supplementary Materials:

Provide downloadable materials for learners to review:

• – PDF Guide: “Coming Soon”
• – Cheat Sheet: “Coming Soon”
• – Video Source: “JNG ACADEMY“
• – Articles: “Blog Page“

FAQs:

More Links:

Paid Earning Courses:

• WordPress for Beginners
• WordPress Freelancing Mastery Course
• Blogging for Beginners

Other Chapters:

1. Numbers and Numeration of Class 5
2. Addition and Subtraction of Class 5
3. Class Notes of Class 5

Share Your Valuable Thoughts:

What’s one real-life situation where you used perimeter or area without realizing it?
Share your thoughts in the comments below — or tell your teacher and classmates in class discussion!