Perimeter (Grade 5)
The perimeter of a shape is the total distance around its boundary. If you walk along the edges of a playground and come back to the starting point, the distance you walk is the perimeter.
Perimeter is one of the most practical measurements in everyday life. Farmers calculate perimeter to know how much fencing to buy. Builders calculate perimeter to determine boundary wall length. Meera might calculate perimeter to know how much ribbon she needs to border a gift.
In Class 5, you will calculate the perimeter of regular and irregular shapes, apply perimeter formulas for common polygons, and solve word problems involving fencing, borders, and boundaries.
What is Perimeter - Class 5 Maths (Measurement)?
The perimeter of a closed figure is the sum of the lengths of all its sides.
For regular shapes, there are shortcut formulas:
Perimeter of Rectangle = 2 × (Length + Breadth)
Perimeter of Square = 4 × Side
Perimeter of Equilateral Triangle = 3 × Side
Perimeter of Regular Polygon = n × Side (where n = number of sides)
Perimeter (Grade 5) Formula
Perimeter Formulas Summary:
| Shape | Formula |
|---|---|
| Any polygon | Sum of all sides |
| Rectangle | 2 × (l + b) |
| Square | 4 × s |
| Equilateral triangle | 3 × s |
| Regular hexagon | 6 × s |
Solved Examples
Example 1: Example 1: Perimeter of a Rectangle
Problem: Find the perimeter of a rectangle with length 15 cm and breadth 8 cm.
Solution:
Step 1: Perimeter = 2 × (Length + Breadth)
Step 2: Perimeter = 2 × (15 + 8) = 2 × 23 = 46 cm
Answer: The perimeter is 46 cm.
Example 2: Example 2: Perimeter of a Square
Problem: A square park has a side of 120 m. Find its perimeter.
Solution:
Step 1: Perimeter = 4 × Side
Step 2: Perimeter = 4 × 120 = 480 m
Answer: The perimeter is 480 m.
Example 3: Example 3: Finding a Missing Side
Problem: The perimeter of a rectangle is 54 cm. The length is 17 cm. Find the breadth.
Solution:
Step 1: Perimeter = 2 × (l + b)
Step 2: 54 = 2 × (17 + b)
Step 3: 27 = 17 + b
Step 4: b = 27 − 17 = 10 cm
Answer: The breadth is 10 cm.
Example 4: Example 4: Fencing Problem
Problem: Arjun wants to put a fence around his rectangular garden that is 25 m long and 15 m wide. If fencing costs ₹80 per metre, find the total cost.
Solution:
Step 1: Perimeter = 2 × (25 + 15) = 2 × 40 = 80 m
Step 2: Cost = Perimeter × Rate = 80 × 80 = ₹6,400
Answer: The total cost of fencing is ₹6,400.
Example 5: Example 5: Perimeter of an Irregular Shape
Problem: An irregular polygon has sides: 5 cm, 7 cm, 3 cm, 9 cm, and 6 cm. Find its perimeter.
Solution:
Step 1: Perimeter = Sum of all sides
Step 2: Perimeter = 5 + 7 + 3 + 9 + 6 = 30 cm
Answer: The perimeter is 30 cm.
Example 6: Example 6: Equilateral Triangle
Problem: An equilateral triangle has a perimeter of 36 cm. Find the length of each side.
Solution:
Step 1: Perimeter of equilateral triangle = 3 × side
Step 2: 36 = 3 × side
Step 3: side = 36 ÷ 3 = 12 cm
Answer: Each side is 12 cm.
Example 7: Example 7: Border Around a Photo
Problem: Meera has a rectangular photo that is 20 cm by 14 cm. She wants to put a ribbon border around it. How much ribbon does she need?
Solution:
Step 1: Ribbon needed = Perimeter of the photo
Step 2: Perimeter = 2 × (20 + 14) = 2 × 34 = 68 cm
Answer: Meera needs 68 cm of ribbon.
Example 8: Example 8: Converting Units
Problem: A rectangular field is 200 m long and 150 m wide. Express its perimeter in kilometres.
Solution:
Step 1: Perimeter = 2 × (200 + 150) = 2 × 350 = 700 m
Step 2: Convert: 700 m = 700 ÷ 1000 = 0.7 km
Answer: The perimeter is 0.7 km.
Example 9: Example 9: Same Perimeter, Different Shapes
Problem: A square and a rectangle both have a perimeter of 40 cm. The square has side 10 cm. If the rectangle has length 12 cm, find its breadth.
Solution:
Step 1: Rectangle perimeter = 40 cm.
Step 2: 2 × (12 + b) = 40
Step 3: 12 + b = 20
Step 4: b = 8 cm
Answer: The breadth of the rectangle is 8 cm.
Example 10: Example 10: Regular Hexagon
Problem: A regular hexagon has a side of 7 cm. Find its perimeter.
Solution:
Step 1: A regular hexagon has 6 equal sides.
Step 2: Perimeter = 6 × 7 = 42 cm
Answer: The perimeter is 42 cm.
Real-World Applications
Where do we use perimeter?
- Fencing: Calculating the total length of wire or fencing needed around a garden, farm, or playground. Arjun’s father calculates perimeter before buying barbed wire for the field.
- Borders: Ribbon around a gift, lace around a tablecloth, decorative tape around a notice board, frame moulding around a picture.
- Running tracks: The distance around the outer edge of a track. One lap = the perimeter of the track.
- Construction: Boundary wall length, plinth band around a building, tile edging around a room.
- Sewing: Piping or lace around the edge of a cushion cover or bedsheet.
- Gardening: How much border edging or stones are needed around a flower bed.
Key Points to Remember
- Perimeter = total distance around a shape = sum of all side lengths.
- Rectangle: Perimeter = 2 × (length + breadth).
- Square: Perimeter = 4 × side.
- Equilateral triangle: Perimeter = 3 × side.
- Regular polygon with n sides: Perimeter = n × side.
- For irregular shapes, add up all the individual side lengths.
- Perimeter is measured in units of length (cm, m, km) — not square units.
Practice Problems
- Find the perimeter of a rectangle with length 22 cm and breadth 13 cm.
- A square has a side of 9.5 cm. What is its perimeter?
- The perimeter of a square is 64 cm. Find the side length.
- The perimeter of a rectangle is 100 m. The length is 30 m. Find the breadth.
- Neha runs around a rectangular park (80 m × 60 m) three times. How far does she run?
- An irregular shape has sides 8 cm, 5 cm, 10 cm, 4 cm, and 7 cm. Find the perimeter.
- A regular pentagon has a perimeter of 55 cm. Find the length of each side.
- Kavi wants to put a border light around his room (6 m × 4.5 m). How many metres of lights does he need?
Frequently Asked Questions
Q1. What is perimeter?
Perimeter is the total distance around the boundary of a closed shape. It is found by adding up the lengths of all the sides.
Q2. What is the formula for the perimeter of a rectangle?
Perimeter of a rectangle = 2 × (length + breadth). This is because a rectangle has two lengths and two breadths.
Q3. What is the difference between perimeter and area?
Perimeter is the distance around the shape (measured in cm, m). Area is the space inside the shape (measured in sq cm, sq m). Perimeter is 1-dimensional; area is 2-dimensional.
Q4. How do you find the perimeter of an irregular shape?
Add up the lengths of all the sides. There is no shortcut formula for irregular shapes — you must know each side length.
Q5. Can two different shapes have the same perimeter?
Yes. For example, a square with side 10 cm (perimeter 40 cm) and a rectangle with length 12 cm and breadth 8 cm (perimeter also 40 cm) have the same perimeter but different shapes.
Q6. What units is perimeter measured in?
Perimeter is measured in units of length: centimetres (cm), metres (m), kilometres (km), etc. It is NOT measured in square units.
Q7. How do I find a missing side if the perimeter is known?
Subtract the sum of the known sides from the total perimeter. For a rectangle: breadth = (perimeter ÷ 2) − length.
Q8. What is the perimeter of a circle called?
The perimeter of a circle is called the circumference. Its formula involves pi and is studied in detail in higher classes.
Q9. Why is perimeter useful in real life?
Perimeter is used to calculate fencing around gardens, border material for frames, the length of a running track, and boundary wall measurements.
Q10. Is perimeter covered in the NCERT Class 5 syllabus?
Yes. Perimeter of regular and irregular shapes is part of the Measurement chapter in NCERT/CBSE Class 5 Maths.
