Introduction to Perimeter
Perimeter is the total distance around the outside of a flat shape. In Class 3, students learn what perimeter means and how to find it by adding the lengths of all sides.
Perimeter is used in real life when fencing a garden, putting ribbon around a card, or building a border around a photo frame.
What is Introduction to Perimeter - Class 3 Maths (Geometry)?
The perimeter of a shape is the total length of its boundary. It is found by adding all the side lengths of the shape.
Perimeter = Sum of all sides
Perimeter is measured in units of length such as cm (centimetres), m (metres), etc.
Types and Properties
Steps to find perimeter:
- Identify all the sides of the shape.
- Measure or note the length of each side.
- Add all the side lengths together.
- Write the answer with the correct unit (cm, m, etc.).
Solved Examples
Example 1: Perimeter of a Triangle
Question: A triangle has sides of 5 cm, 7 cm, and 6 cm. Find its perimeter.
Think:
- Perimeter = 5 + 7 + 6 = 18 cm
Answer: The perimeter is 18 cm.
Example 2: Perimeter of a Rectangle
Question: A rectangle has a length of 8 cm and a breadth of 4 cm. Find its perimeter.
Think:
- A rectangle has 2 lengths and 2 breadths.
- Perimeter = 8 + 4 + 8 + 4 = 24 cm
Answer: The perimeter is 24 cm.
Example 3: Perimeter of a Square
Question: A square has each side 6 cm. Find its perimeter.
Think:
- A square has 4 equal sides.
- Perimeter = 6 + 6 + 6 + 6 = 24 cm
Answer: The perimeter is 24 cm.
Example 4: Perimeter of an Irregular Shape
Question: A shape has 5 sides with lengths 3 cm, 4 cm, 5 cm, 2 cm, and 6 cm. Find its perimeter.
Think:
- Perimeter = 3 + 4 + 5 + 2 + 6 = 20 cm
Answer: The perimeter is 20 cm.
Example 5: Word Problem - Fencing a Garden
Question: Aman's garden is shaped like a rectangle with length 10 m and breadth 6 m. How much fencing does he need?
Think:
- Fencing goes around the outside = perimeter
- Perimeter = 10 + 6 + 10 + 6 = 32 m
Answer: Aman needs 32 m of fencing.
Example 6: Word Problem - Ribbon Around a Card
Question: Priya puts ribbon around a square greeting card. Each side is 12 cm. How much ribbon does she need?
Think:
- Perimeter of square = 12 + 12 + 12 + 12 = 48 cm
Answer: Priya needs 48 cm of ribbon.
Example 7: Finding a Missing Side
Question: A rectangle has a perimeter of 20 cm. Its length is 7 cm. Find the breadth.
Think:
- Perimeter = 7 + breadth + 7 + breadth = 20
- 14 + 2 x breadth = 20
- 2 x breadth = 6
- Breadth = 3 cm
Answer: The breadth is 3 cm.
Example 8: Perimeter on a Grid
Question: A shape is drawn on a 1 cm grid. It covers the outline of 4 squares across and 3 squares down (a 4 x 3 rectangle). Find the perimeter.
Think:
- Length = 4 cm, Breadth = 3 cm
- Perimeter = 4 + 3 + 4 + 3 = 14 cm
Answer: The perimeter is 14 cm.
Example 9: Comparing Perimeters
Question: Shape A is a square with side 5 cm. Shape B is a rectangle with length 6 cm and breadth 3 cm. Which has a larger perimeter?
Think:
- Perimeter of A = 4 x 5 = 20 cm
- Perimeter of B = 6 + 3 + 6 + 3 = 18 cm
- 20 > 18
Answer: Shape A (the square) has a larger perimeter by 2 cm.
Key Points to Remember
- Perimeter is the total distance around a shape.
- To find perimeter, add all the side lengths.
- Perimeter is measured in units of length: cm, m, etc.
- For a rectangle: Perimeter = length + breadth + length + breadth.
- For a square: Perimeter = 4 times the side length.
- Perimeter is used for fencing, bordering, and framing.
- If perimeter and some sides are known, the missing side can be found by subtraction.
Practice Problems
- Find the perimeter of a triangle with sides 4 cm, 6 cm, and 5 cm.
- A square has a side of 9 cm. What is its perimeter?
- A rectangle has a length of 12 cm and a breadth of 5 cm. Find its perimeter.
- Meera wants to put lace around a rectangular tablecloth that is 80 cm long and 50 cm wide. How much lace does she need?
- A shape has sides 3 cm, 5 cm, 4 cm, and 6 cm. Find the perimeter.
- A square garden has a perimeter of 40 m. What is the length of one side?
- Dev draws a rectangle with a perimeter of 30 cm. The length is 9 cm. Find the breadth.
Frequently Asked Questions
Q1. What is perimeter?
Perimeter is the total distance around the boundary of a flat shape. It is found by adding the lengths of all the sides.
Q2. How do you find the perimeter of any shape?
Add all the side lengths together. For a triangle with sides 3, 4, and 5 cm, the perimeter is 3 + 4 + 5 = 12 cm.
Q3. What unit is perimeter measured in?
Perimeter is measured in units of length such as centimetres (cm), metres (m), or kilometres (km), depending on the size of the shape.
Q4. What is the difference between perimeter and area?
Perimeter is the distance around a shape (measured in cm, m). Area is the space inside a shape (measured in sq cm, sq m). In Class 3, students mainly learn perimeter.
Q5. How do you find a missing side if perimeter is given?
Add the known sides and subtract from the total perimeter. For example, if a triangle has perimeter 15 cm and two sides are 4 cm and 6 cm, the third side is 15 minus 10 = 5 cm.
Q6. Where is perimeter used in real life?
Perimeter is used when fencing a garden, putting ribbon around a card, framing a picture, or measuring the boundary of a playground.
Q7. Can two shapes have the same perimeter but look different?
Yes. A square with side 4 cm (perimeter 16 cm) and a rectangle with length 5 cm and breadth 3 cm (perimeter 16 cm) both have the same perimeter but different shapes.
Q8. Is perimeter taught in NCERT Class 3?
Yes. Introduction to perimeter is part of the Geometry chapter in NCERT Class 3 Maths. Students learn to calculate perimeter by adding side lengths.
