Perimeter of Triangle
The perimeter of a triangle is the total distance around the triangle. Since a triangle has 3 sides, you find the perimeter by adding the lengths of all three sides.
In Class 3, you learn to calculate the perimeter of different types of triangles — equilateral (all sides equal), isosceles (two sides equal), and scalene (all sides different).
Perimeter is measured in units of length like centimetres (cm) or metres (m).
What is Perimeter of Triangle - Class 3 Maths (Geometry (Grade 3))?
Perimeter of a Triangle = Side 1 + Side 2 + Side 3
For special triangles:
- Equilateral triangle (all 3 sides equal): Perimeter = 3 × side
- Isosceles triangle (2 sides equal): Perimeter = 2 × equal side + base
- Scalene triangle (all sides different): Perimeter = a + b + c
Types and Properties
Types of Triangles and Their Perimeters
| Triangle Type | Sides | Perimeter Formula |
|---|---|---|
| Equilateral | All 3 sides equal | 3 × side |
| Isosceles | 2 sides equal | 2 × equal side + base |
| Scalene | All sides different | a + b + c |
Solved Examples
Example 1: Example 1: Scalene Triangle
Question: A triangle has sides 7 cm, 9 cm, and 12 cm. Find its perimeter.
Think:
- Perimeter = 7 + 9 + 12 = 28 cm
Answer: Perimeter = 28 cm
Example 2: Example 2: Equilateral Triangle
Question: An equilateral triangle has a side of 10 cm. Find its perimeter.
Think:
- All sides are 10 cm
- Perimeter = 3 × 10 = 30 cm
Answer: Perimeter = 30 cm
Example 3: Example 3: Isosceles Triangle
Question: An isosceles triangle has two equal sides of 8 cm each and a base of 6 cm. Find its perimeter.
Think:
- Perimeter = 8 + 8 + 6 = 22 cm
- Or: 2 × 8 + 6 = 22 cm
Answer: Perimeter = 22 cm
Example 4: Example 4: Word Problem – Garden
Question: Aman has a triangular garden with sides 15 m, 12 m, and 10 m. He wants to put a fence around it. How much fencing does he need?
Think:
- Perimeter = 15 + 12 + 10 = 37 m
Answer: Aman needs 37 m of fencing.
Example 5: Example 5: Finding a Missing Side
Question: A triangle has a perimeter of 24 cm. Two sides are 8 cm and 9 cm. Find the third side.
Think:
- Third side = Perimeter − (side 1 + side 2)
- Third side = 24 − (8 + 9) = 24 − 17 = 7 cm
Answer: The third side is 7 cm.
Example 6: Example 6: Cost of Fencing
Question: A triangular plot has sides 20 m, 25 m, and 30 m. Fencing costs ₹8 per metre. What is the total cost?
Think:
- Perimeter = 20 + 25 + 30 = 75 m
- Cost = 75 × 8 = ₹600
Answer: Total cost = ₹600
Example 7: Example 7: Comparing Perimeters
Question: Triangle A has sides 5 cm, 5 cm, 5 cm. Triangle B has sides 4 cm, 6 cm, 7 cm. Which has a greater perimeter?
Think:
- Perimeter A = 5 + 5 + 5 = 15 cm
- Perimeter B = 4 + 6 + 7 = 17 cm
Answer: Triangle B has a greater perimeter (17 cm > 15 cm).
Example 8: Example 8: Wire Bent into a Triangle
Question: Priya bends a wire of length 36 cm into an equilateral triangle. What is the length of each side?
Think:
- Perimeter = 36 cm
- Equilateral → 3 equal sides
- Side = 36 ÷ 3 = 12 cm
Answer: Each side is 12 cm.
Example 9: Example 9: Border Around a Triangular Card
Question: Aditi makes a triangular card with sides 14 cm, 14 cm, and 10 cm. She puts glitter tape around the border. How much tape does she need?
Think:
- Perimeter = 14 + 14 + 10 = 38 cm
Answer: Aditi needs 38 cm of tape.
Example 10: Example 10: Multiple Triangles
Question: Rahul draws 3 equilateral triangles, each with a side of 6 cm. What is the total perimeter of all three?
Think:
- Perimeter of one = 3 × 6 = 18 cm
- Total for 3 triangles = 3 × 18 = 54 cm
Answer: Total perimeter = 54 cm
Real-World Applications
Where Do We Find Perimeters of Triangles?
- Fencing: Triangular plots and gardens need fencing along all three sides.
- Art: Making triangular frames, borders, and decorations.
- Road signs: Many road signs are triangular — their edges have a measurable perimeter.
- Architecture: Triangular roofs and supports use perimeter calculations.
- Sports: Triangular areas on courts and fields.
Key Points to Remember
- Perimeter of any triangle = sum of all 3 sides.
- Equilateral triangle: Perimeter = 3 × side.
- Isosceles triangle: Perimeter = 2 × equal side + base.
- Scalene triangle: add all three different sides.
- To find a missing side: Perimeter − sum of known sides.
- Cost of fencing = Perimeter × cost per unit length.
- If a wire is bent into an equilateral triangle: side = wire length ÷ 3.
Practice Problems
- A triangle has sides 11 cm, 13 cm, and 15 cm. Find its perimeter.
- An equilateral triangle has a side of 9 cm. Find its perimeter.
- An isosceles triangle has equal sides of 12 cm and a base of 8 cm. Find the perimeter.
- A triangle has a perimeter of 40 cm. Two sides are 15 cm and 12 cm. Find the third side.
- Dev bends a 42 cm wire into an equilateral triangle. What is each side?
- A triangular park has sides 50 m, 40 m, and 35 m. How much fencing is needed?
- Ria makes 4 identical triangles with sides 5 cm, 5 cm, 8 cm each. What is the total perimeter?
Frequently Asked Questions
Q1. What is the perimeter of a triangle?
The perimeter of a triangle is the total distance around it, found by adding the lengths of all three sides.
Q2. What is the formula for the perimeter of an equilateral triangle?
Perimeter = 3 × side, because all three sides are equal.
Q3. How do I find a missing side of a triangle if I know the perimeter?
Subtract the sum of the two known sides from the perimeter. Missing side = Perimeter − (side 1 + side 2).
Q4. What is an equilateral triangle?
An equilateral triangle has all three sides of equal length. All its angles are also equal (60° each).
Q5. What is an isosceles triangle?
An isosceles triangle has exactly two sides of equal length. The third side (base) is different.
Q6. What is a scalene triangle?
A scalene triangle has all three sides of different lengths. No two sides are equal.
Q7. What units are used for perimeter?
Perimeter is measured in the same units as the sides — centimetres (cm), metres (m), or any other unit of length.
Q8. Can a triangle have a perimeter of 0?
No. A triangle must have three sides with positive lengths, so its perimeter is always greater than 0.
Q9. If I bend a wire into a triangle, what is the perimeter?
The perimeter equals the length of the wire. If the wire is 30 cm, the perimeter of the triangle is 30 cm.
