How to Find the Perimeter of a Triangle: Step-by-Step Guide
The concept of Perimeter of Triangle plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding how to calculate the perimeter of a triangle helps students solve geometry questions quickly and is frequently required in classwork, competitive exams, and everyday measurement tasks.
What Is Perimeter of Triangle?
The perimeter of a triangle is defined as the total length of its boundary, found by adding together the measures of its three sides. You’ll find this concept applied in areas such as fencing a triangular garden, coordinate geometry, and practical exam problem-solving.
Key Formula for Perimeter of Triangle
Here’s the standard formula: \( Perimeter = a + b + c \), where \( a, b, c \) are the triangle’s side lengths in the same units (like cm or m).
Cross-Disciplinary Usage
Perimeter of triangle is not only useful in Maths but also plays an important role in Physics (when calculating paths), Computer Science (geometry algorithms), and daily logical reasoning. Students preparing for exams like CBSE, JEE, or Olympiads will see its relevance in many questions.
Step-by-Step Illustration
- Start with the given triangle side lengths: Suppose sides \( a = 5\ \text{cm} \), \( b = 7\ \text{cm} \), \( c = 6\ \text{cm} \).
- Add all three sides:
- Final Answer: Perimeter = 18 cm
Types of Triangles & Formulas
| Triangle Type | Formula | Example |
|---|---|---|
| Scalene | a + b + c | Sides: 3, 5, 7 → 15 units |
| Isosceles | 2a + b | Sides: 6, 6, 8 → 6+6+8=20 units |
| Equilateral | 3a | Sides: 4, 4, 4 → 12 units |
| Right-angled | a + b + h (use h = √(a² + b²) if needed) | Sides: 3, 4, 5 → 12 units |
Speed Trick or Vedic Shortcut
For equilateral triangles, just remember: since all sides are equal, multiply one side by 3 for the perimeter. This works fast for MCQs!
Example Trick: If a triangle has sides of 10 cm (all equal), its perimeter is 10 × 3 = 30 cm.
Worked Examples
Example 1: Perimeter with 3 Sides
If a triangle has sides 6 cm, 8 cm, and 10 cm, then:
1. Add: 6 + 8 + 10 = 242. Final Answer: Perimeter = 24 cm
Example 2: Find Missing Side when Perimeter is Known
Triangle perimeter = 30 cm. Two sides are 11 cm and 9 cm. Find the third side.
1. Let missing side = x2. \( 11 + 9 + x = 30 \)
3. \( x = 30 - 20 = 10 \) cm
4. The missing side = 10 cm
Example 3: Perimeter Using Coordinates
For points A(0,0), B(0,6), C(8,0),
1. Use distance formula for each side:- AB = |6-0| = 6
- BC = √[(8-0)² + (0-6)²] = √[64 + 36] = √100 = 10
- CA = |8-0| = 8
2. Total perimeter: 6 + 10 + 8 = 24 units
3. Perimeter = 24 units
Try These Yourself
- Find the perimeter of a triangle with sides 4 cm, 7 cm, 5 cm.
- A triangle’s perimeter is 21 cm. Two sides are 8 cm and 6 cm. What’s the third side?
- What is the perimeter of an equilateral triangle with a 9 cm side?
- If triangle coordinates are (2,3), (2,7), (6,3), find the perimeter.
Frequent Errors and Misunderstandings
- Forgetting to use the same units on all side lengths.
- Mixing up perimeter and area (remember: perimeter is boundary length, area is surface covered).
- Using the wrong formula for isosceles or equilateral triangles.
- Missing “find the missing side” in word problems and not subtracting properly.
Relation to Other Concepts
The idea of perimeter of triangle connects closely with Area of Triangle and Perimeter and Area of Plane Figures. Mastering this helps with understanding polygons, quadrilaterals, and more advanced geometry problems. Explore more on Types of Triangles to apply correct formulas in exams.
Classroom Tip
A quick way to remember perimeter of triangle is: “Perimeter = Add All Sides.” Use a simple chant: “Perimeter is all around, add each side that you have found!” Vedantu’s teachers often use real examples—like fencing a playground in the shape of a triangle—to make this concept easy during live classes.
We explored perimeter of triangle—from definition, formula, examples, mistakes, and connections to other subjects. Continue practicing with Vedantu to become confident in solving problems using this concept.
Related Reading: Area of Triangle | Types of Triangles | Perimeter of Square | Perimeter and Area of Plane Figures
FAQs on Perimeter of a Triangle: Definition, Formula & Solved Problems
1. What is the perimeter of a triangle?
The perimeter of a triangle is the total distance around its three sides. It's the sum of the lengths of all three sides.
2. How do you calculate the perimeter of a triangle if you know all three sides?
Simply add the lengths of the three sides together. The formula is: Perimeter = a + b + c, where 'a', 'b', and 'c' represent the lengths of the three sides.
3. What is the formula for the perimeter of an equilateral triangle?
In an equilateral triangle, all three sides are equal. Therefore, the perimeter is three times the length of one side: Perimeter = 3a, where 'a' is the length of one side.
4. What is the perimeter of an isosceles triangle?
An isosceles triangle has two equal sides. The perimeter is calculated as: Perimeter = 2a + b, where 'a' is the length of each of the equal sides, and 'b' is the length of the third side.
5. How do you find the perimeter of a right-angled triangle?
For a right-angled triangle, add the lengths of the two shorter sides (legs) and the hypotenuse. If you only know two sides, use the Pythagorean theorem (a² + b² = c²) to find the missing side before calculating the perimeter.
6. Can you find the perimeter if only two sides are given?
No, you cannot find the perimeter of a triangle if only two sides are given. You need all three side lengths. However, if it's a right-angled triangle and you know two sides, you can use the Pythagorean theorem to find the third side and then calculate the perimeter.
7. How is the perimeter formula used in coordinate geometry problems?
In coordinate geometry, you first find the lengths of the sides using the distance formula. Then, you use the standard perimeter formula (a + b + c) to find the perimeter.
8. What are some common mistakes students make when calculating the perimeter of a triangle?
Common mistakes include forgetting to add all three sides, misusing units, and incorrectly applying the Pythagorean theorem in right-angled triangles. Always double-check your calculations and units.
9. Is the perimeter of a triangle the same as its area?
No, perimeter and area are different. The perimeter is the total distance around the triangle, while the area measures the space inside the triangle. They are calculated using different formulas.
10. How can I find a missing side of a triangle if I know the perimeter and the other two sides?
Subtract the lengths of the two known sides from the total perimeter. The result is the length of the missing side. For example, if the perimeter is 20 cm and two sides are 6 cm and 8 cm, the missing side is 20 - 6 - 8 = 6 cm.
11. What are real-world applications of calculating the perimeter of a triangle?
Calculating the perimeter of a triangle is useful in various real-world situations, including fencing a triangular garden, calculating the amount of material needed for a triangular sail, or determining the distance around a triangular piece of land.
