Perimeter (Grade 4)
The perimeter of a shape is the total distance around its boundary. If you walk along the edges of a playground, the total distance you cover is its perimeter.
In Class 4, you will learn to find the perimeter of rectangles, squares, triangles, and irregular shapes by adding the lengths of all sides.
What is Perimeter - Class 4 Maths (Measurement)?
Perimeter is the total length of the boundary of a closed shape. It is found by adding the lengths of all sides.
Perimeter is measured in units of length — cm, m, or km.
Perimeter (Grade 4) Formula
Perimeter of Rectangle = 2 × (Length + Breadth)
Perimeter of Square = 4 × Side
Perimeter of Triangle = Side 1 + Side 2 + Side 3
For any shape, the perimeter = sum of all sides.
Types and Properties
Regular shapes have all sides equal — use a shortcut formula (multiply side × number of sides).
Irregular shapes have different side lengths — add each side individually.
| Shape | Formula |
|---|---|
| Rectangle | 2 × (l + b) |
| Square | 4 × s |
| Equilateral triangle | 3 × s |
| Regular pentagon | 5 × s |
| Regular hexagon | 6 × s |
| Any shape | Add all sides |
Solved Examples
Example 1: Example 1: Perimeter of a rectangle
Problem: Find the perimeter of a rectangle with length 12 cm and breadth 8 cm.
Solution:
Step 1: Perimeter = 2 × (Length + Breadth)
Step 2: Perimeter = 2 × (12 + 8) = 2 × 20 = 40 cm
Answer: The perimeter is 40 cm.
Example 2: Example 2: Perimeter of a square
Problem: Find the perimeter of a square with side 9 cm.
Solution:
Step 1: Perimeter = 4 × Side
Step 2: Perimeter = 4 × 9 = 36 cm
Answer: The perimeter is 36 cm.
Example 3: Example 3: Perimeter of a triangle
Problem: A triangle has sides 7 cm, 10 cm, and 12 cm. Find its perimeter.
Solution:
Step 1: Perimeter = 7 + 10 + 12 = 29 cm
Answer: The perimeter is 29 cm.
Example 4: Example 4: Fencing a garden
Problem: Aman wants to put a fence around his rectangular garden that is 20 m long and 15 m wide. How much fencing does he need?
Solution:
Step 1: Fencing = Perimeter of the rectangle.
Step 2: Perimeter = 2 × (20 + 15) = 2 × 35 = 70 m
Answer: Aman needs 70 m of fencing.
Example 5: Example 5: Finding a missing side
Problem: The perimeter of a rectangle is 50 cm. The length is 15 cm. Find the breadth.
Solution:
Step 1: Perimeter = 2 × (Length + Breadth)
Step 2: 50 = 2 × (15 + Breadth)
Step 3: 50 ÷ 2 = 25 → 15 + Breadth = 25
Step 4: Breadth = 25 − 15 = 10 cm
Answer: The breadth is 10 cm.
Example 6: Example 6: Equilateral triangle
Problem: Each side of an equilateral triangle is 11 cm. Find the perimeter.
Solution:
Step 1: All 3 sides are equal.
Step 2: Perimeter = 3 × 11 = 33 cm
Answer: The perimeter is 33 cm.
Example 7: Example 7: Irregular shape
Problem: An L-shaped figure has sides: 4 cm, 2 cm, 2 cm, 3 cm, 2 cm, and 5 cm. Find its perimeter.
Solution:
Step 1: Add all sides: 4 + 2 + 2 + 3 + 2 + 5 = 18 cm
Answer: The perimeter of the L-shape is 18 cm.
Example 8: Example 8: Perimeter of a regular hexagon
Problem: A regular hexagonal rangoli has each side 6 cm. Find the perimeter.
Solution:
Step 1: A regular hexagon has 6 equal sides.
Step 2: Perimeter = 6 × 6 = 36 cm
Answer: The perimeter is 36 cm.
Example 9: Example 9: Cost of fencing
Problem: Priya wants to put a ribbon border around a square card of side 14 cm. Ribbon costs ₹2 per cm. What is the total cost?
Solution:
Step 1: Perimeter = 4 × 14 = 56 cm
Step 2: Cost = 56 × ₹2 = ₹112
Answer: The total cost is ₹112.
Example 10: Example 10: Comparing perimeters
Problem: Shape A is a rectangle (10 cm × 5 cm). Shape B is a square (7 cm). Which has a greater perimeter?
Solution:
Step 1: Perimeter of A = 2 × (10 + 5) = 30 cm
Step 2: Perimeter of B = 4 × 7 = 28 cm
Step 3: 30 > 28
Answer: The rectangle has a greater perimeter (30 cm vs 28 cm).
Real-World Applications
Perimeter is used in many real-life situations:
- Fencing — to know how much fencing material to buy for a garden or field.
- Framing — to find the length of frame needed for a picture or mirror.
- Ribbon and border — to measure how much ribbon to wrap around a card or gift.
- Running tracks — the distance around a track is its perimeter.
Key Points to Remember
- Perimeter = total distance around a shape = sum of all sides.
- Rectangle: Perimeter = 2 × (l + b).
- Square: Perimeter = 4 × side.
- Triangle: Perimeter = sum of 3 sides.
- Regular polygon: Perimeter = number of sides × length of one side.
- For irregular shapes, add each side individually.
- Perimeter is measured in cm, m, or km (units of length, not square units).
Practice Problems
- Find the perimeter of a rectangle with length 18 cm and breadth 11 cm.
- A square has a perimeter of 48 cm. Find the length of each side.
- A triangle has sides 8 cm, 15 cm, and 17 cm. Find its perimeter.
- Dev wants to put a wire border around a rectangular board that is 30 cm by 20 cm. How much wire does he need?
- The perimeter of a rectangle is 60 m. If the length is 18 m, find the breadth.
- An equilateral triangle and a square have the same perimeter of 36 cm. Find the side of each.
- Neha walks around a rectangular park 3 times. The park is 200 m long and 100 m wide. What total distance does she walk?
Frequently Asked Questions
Q1. What is perimeter?
Perimeter is the total distance around the boundary of a closed shape. It is found by adding the lengths of all sides.
Q2. What is the formula for the perimeter of a rectangle?
Perimeter of a rectangle = 2 × (Length + Breadth). This works because a rectangle has two pairs of equal opposite sides.
Q3. What unit is perimeter measured in?
Perimeter is measured in units of length — centimetres (cm), metres (m), or kilometres (km). It is NOT measured in square units.
Q4. How is perimeter different from 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). Perimeter is a line measurement; area is a surface measurement.
Q5. Can two different shapes have the same perimeter?
Yes. A rectangle of 10 cm × 5 cm (perimeter 30 cm) and a square of 7.5 cm (perimeter 30 cm) have the same perimeter but different shapes and areas.
Q6. How do you find the perimeter of an irregular shape?
Measure each side and add all the measurements together. There is no shortcut formula for irregular shapes.
Q7. How do you find a missing side if you know the perimeter?
Subtract the sum of the known sides from the total perimeter. For a rectangle with perimeter P and length l: breadth = (P ÷ 2) − l.
Q8. What is the perimeter of a circle called?
The perimeter of a circle is called the circumference. You will learn to calculate it in higher classes using the formula C = 2 × pi × r.
Related Topics
- Perimeter of Rectangle
- Introduction to Area
- Area of Rectangle (Grade 4)
- Area of Square (Grade 4)
- Area and Perimeter Word Problems (Grade 4)
- Converting Units of Length (Grade 4)
- Converting Units of Weight (Grade 4)
- Converting Units of Capacity (Grade 4)
- Area by Counting Squares
- Perimeter of Irregular Shapes
- Relationship Between Area and Perimeter
