Perimeter Word Problems (Grade 3)
Perimeter is the total distance around a shape. In Class 3, you solve word problems about fencing gardens, framing pictures, putting borders on cards, and walking around parks.
Perimeter word problems combine your knowledge of addition, multiplication, and the perimeter formulas for rectangles, squares, and triangles.
The key idea: add all the side lengths to find the perimeter.
What is Perimeter Word Problems - Class 3 Maths (Geometry (Grade 3))?
Perimeter = the total length of all sides of a shape added together.
Perimeter of Rectangle = 2 × (Length + Breadth)
Perimeter of Square = 4 × Side
Perimeter of Triangle = Side 1 + Side 2 + Side 3
Types and Properties
Types of Perimeter Word Problems
1. Fencing Problems
Find the length of fencing needed around a garden or field.
2. Border/Frame Problems
Find the length of border tape or frame needed around a picture or card.
3. Walking/Running Around Problems
Find the distance covered when someone walks around a park or playground.
4. Finding a Missing Side
Given the perimeter and some sides, find the missing side length.
Solved Examples
Example 1: Example 1: Fencing a Rectangular Garden
Question: Aman's garden is 12 m long and 8 m wide. How much fencing does he need?
Think:
- Perimeter = 2 × (12 + 8) = 2 × 20 = 40 m
Answer: Aman needs 40 m of fencing.
Example 2: Example 2: Framing a Square Photo
Question: Priya wants to put a frame around a square photo with side 15 cm. How much frame material does she need?
Think:
- Perimeter of square = 4 × 15 = 60 cm
Answer: Priya needs 60 cm of frame material.
Example 3: Example 3: Walking Around a Park
Question: A rectangular park is 50 m long and 30 m wide. Rahul walks around it 2 times. How far does he walk?
Think:
- Perimeter = 2 × (50 + 30) = 2 × 80 = 160 m
- Two rounds = 160 × 2 = 320 m
Answer: Rahul walks 320 m.
Example 4: Example 4: Triangular Sign
Question: A triangular road sign has sides of 20 cm, 20 cm, and 25 cm. What is its perimeter?
Think:
- Perimeter = 20 + 20 + 25 = 65 cm
Answer: The perimeter is 65 cm.
Example 5: Example 5: Border for a Card
Question: Aditi makes a greeting card that is 20 cm long and 14 cm wide. She puts a ribbon border around it. How much ribbon does she need?
Think:
- Perimeter = 2 × (20 + 14) = 2 × 34 = 68 cm
Answer: Aditi needs 68 cm of ribbon.
Example 6: Example 6: Finding a Missing Side
Question: A rectangle has a perimeter of 30 cm. Its length is 9 cm. What is its breadth?
Think:
- Perimeter = 2 × (L + B)
- 30 = 2 × (9 + B)
- 9 + B = 15
- B = 15 − 9 = 6 cm
Answer: The breadth is 6 cm.
Example 7: Example 7: Cost of Fencing
Question: A square playground has a side of 25 m. Fencing costs ₹10 per metre. What is the total cost of fencing?
Think:
- Perimeter = 4 × 25 = 100 m
- Cost = 100 × 10 = ₹1000
Answer: The total cost is ₹1000.
Example 8: Example 8: Comparing Perimeters
Question: Rectangle A is 10 cm × 5 cm. Rectangle B is 8 cm × 7 cm. Which has a greater perimeter?
Think:
- Perimeter A = 2 × (10 + 5) = 30 cm
- Perimeter B = 2 × (8 + 7) = 30 cm
Answer: Both rectangles have the same perimeter of 30 cm.
Example 9: Example 9: Irregular Shape
Question: A garden has 5 sides of lengths 6 m, 4 m, 5 m, 3 m, and 7 m. What is its perimeter?
Think:
- Add all sides: 6 + 4 + 5 + 3 + 7 = 25 m
Answer: The perimeter is 25 m.
Example 10: Example 10: Finding Side of a Square
Question: The perimeter of a square is 48 cm. What is the length of each side?
Think:
- Perimeter = 4 × side
- 48 = 4 × side
- Side = 48 ÷ 4 = 12 cm
Answer: Each side is 12 cm.
Real-World Applications
Where Do We Use Perimeter in Daily Life?
- Fencing: Calculating how much wire or fencing is needed around a garden.
- Framing: Finding the length of frame material for a photo or painting.
- Borders: Measuring border tape for a bulletin board or card.
- Running track: Calculating the distance of one lap around a field.
- Construction: Measuring the boundary of a plot for a wall or fence.
Key Points to Remember
- Perimeter = sum of all side lengths.
- Rectangle perimeter = 2 × (L + B).
- Square perimeter = 4 × side.
- Triangle perimeter = sum of 3 sides.
- If someone walks around a shape multiple times, multiply perimeter by the number of rounds.
- To find cost of fencing: Perimeter × cost per metre.
- To find a missing side: rearrange the perimeter formula.
Practice Problems
- A rectangular field is 40 m long and 25 m wide. How much fencing is needed?
- A square table top has a side of 80 cm. What is its perimeter?
- Meera walks around a rectangular park (60 m × 40 m) 3 times. How far does she walk?
- A triangle has sides 12 cm, 15 cm, and 18 cm. Find its perimeter.
- A rectangle has a perimeter of 50 cm and a length of 15 cm. Find its breadth.
- Kavi wants to put a border around a square card with side 12 cm. The border tape costs ₹2 per cm. What is the total cost?
- A playground has 4 sides: 20 m, 35 m, 20 m, and 35 m. What shape is it? Find its perimeter.
Frequently Asked Questions
Q1. What is perimeter?
Perimeter is the total distance around the outside of a shape. It is found by adding the lengths of all the sides.
Q2. How do I find the perimeter of a rectangle?
Use the formula: Perimeter = 2 × (Length + Breadth). Add the length and breadth, then multiply by 2.
Q3. What is the unit of perimeter?
Perimeter is measured in units of length — centimetres (cm), metres (m), or kilometres (km), depending on the size of the shape.
Q4. How do I find a missing side if I know the perimeter?
Subtract the known sides from the perimeter. For a rectangle: Breadth = (Perimeter ÷ 2) − Length.
Q5. Can two different shapes have the same perimeter?
Yes. For example, a 10 cm × 5 cm rectangle and an 8 cm × 7 cm rectangle both have a perimeter of 30 cm.
Q6. How do I calculate cost of fencing?
First find the perimeter, then multiply by the cost per unit length. For example, if perimeter = 40 m and cost = ₹5 per m, total cost = 40 × 5 = ₹200.
Q7. Is perimeter the same as area?
No. Perimeter is the distance around a shape (measured in cm, m). Area is the space inside a shape (measured in sq cm, sq m). They are different measurements.
Q8. What if someone walks around a shape more than once?
Multiply the perimeter by the number of rounds. If the perimeter is 100 m and someone walks 3 rounds, the total distance is 300 m.
Q9. How do I find the perimeter of an irregular shape?
Measure all the sides and add them up. There is no shortcut formula for irregular shapes.
