Triangle Perimeter Practice Problems - Calculator & Examples

Master triangle perimeter calculations with step-by-step practice problems. Learn formulas for equilateral, isosceles, and scalene triangles with instant feedback.

📚What You'll Master in This Practice Session
  • Calculate perimeter using the formula P = Side 1 + Side 2 + Side 3
  • Solve equilateral triangle problems when only one side length is given
  • Find missing sides in isosceles triangles using perimeter relationships
  • Apply Pythagorean theorem to find unknown sides before calculating perimeter
  • Work backwards from perimeter to determine individual side lengths
  • Compare perimeters of different geometric shapes including triangles and circles

Understanding Perimeter of a Triangle

Complete explanation with examples

Perimeter: calculating the perimeter of a triangle

To calculate the perimeter of a triangle, all you have to do is add its three sides. If you have all the necessary information, you can solve such a problem in a matter of seconds, for example:

Formula for the perimeter of a triangle:

P = Side 1 + Side 2 + Side 3.

A - The formula of the perimeter of a triangle

If you give us a triangle whose sides have the following measurements:

AB=5 AB = 5

BC=8 BC = 8

CA=6 CA = 6

In this case, the perimeter of the triangle, which is the sum of the 3 3 sides will be equal to. 19 19

Detailed explanation

Practice Perimeter of a Triangle

Test your knowledge with 4 quizzes

Below is the right triangle ABD, which has a perimeter of 36 cm.

AB = 15

AC = 13

DC = 5

CB = 4

Work out the area of the triangle.

151515444555131313BBBCCCDDDAAA

Examples with solutions for Perimeter of a Triangle

Step-by-step solutions included
Exercise #1

Look at the triangle below:

666888101010

What is the perimeter of the triangle?

Step-by-Step Solution

The perimeter of the triangle is equal to the sum of all sides together, therefore:

6+8+10=14+10=24 6+8+10=14+10=24

Answer:

24

Video Solution
Exercise #2

Given the triangle:

777111111131313

What is its perimeter?

Step-by-Step Solution

The perimeter of a triangle is equal to the sum of all its sides together:

11+7+13=11+20=31 11+7+13=11+20=31

Answer:

31

Video Solution
Exercise #3

Find the perimeter of the triangle ABC

777141414888AAABBBCCC

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the given information.
  • Step 2: Apply the perimeter formula for a triangle.
  • Step 3: Perform the addition to find the perimeter.

Now, let's work through each step:

Step 1: We have the lengths of the sides of ABC \triangle ABC as follows:
AB=7 AB = 7 , BC=14 BC = 14 , and CA=8 CA = 8 .

Step 2: We'll use the formula for the perimeter of a triangle, which is the sum of its side lengths:
P=AB+BC+CA P = AB + BC + CA .

Step 3: Plugging in the values, we calculate:
P=7+14+8=29 P = 7 + 14 + 8 = 29 .

Therefore, the perimeter of ABC \triangle ABC is 29\textbf{29}.

Answer:

29

Video Solution
Exercise #4

Find the perimeter of the triangle ABC

333444555AAABBBCCC

Step-by-Step Solution

To find the perimeter of triangle ABC \triangle ABC , we need to sum the lengths of its sides:

  • Side AB=3 AB = 3
  • Side BC=4 BC = 4
  • Side CA=5 CA = 5

Using the formula for the perimeter of a triangle:

Perimeter=AB+BC+CA \text{Perimeter} = AB + BC + CA

Substitute the known values:

Perimeter=3+4+5 \text{Perimeter} = 3 + 4 + 5

Perimeter=12 \text{Perimeter} = 12

Thus, the perimeter of triangle ABC \triangle ABC is 12\mathbf{12}.

From the multiple-choice options provided, the correct choice is option 1: 12.

Answer:

12

Video Solution
Exercise #5

Given an equilateral triangle:

555

What is its perimeter?

Step-by-Step Solution

Since the triangle is equilateral, that is, all sides are equal to each other.

The perimeter of the triangle is equal to the sum of all sides together, the perimeter of the triangle in the drawing is equal to:

5+5+5=15 5+5+5=15

Answer:

15

Video Solution

Frequently Asked Questions

What is the formula for finding the perimeter of any triangle?

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The perimeter formula for any triangle is P = Side 1 + Side 2 + Side 3. Simply add all three side lengths together to get the total distance around the triangle.

How do you find the perimeter of an equilateral triangle with one side?

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Since all sides of an equilateral triangle are equal, multiply the known side length by 3. For example, if one side is 4 units, the perimeter is 4 × 3 = 12 units.

What steps should I follow when the triangle perimeter problem doesn't give all side lengths?

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Follow these steps: 1) Identify what information you have and what you need to find, 2) Use triangle properties (equilateral, isosceles, scalene) to determine missing sides, 3) Apply relevant formulas like Pythagorean theorem if needed, 4) Add all three sides to calculate perimeter.

How do you solve isosceles triangle perimeter problems?

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Remember that isosceles triangles have two equal sides. If you know one of the equal sides and the perimeter, subtract twice the known side from the total perimeter to find the base. If you know the base and perimeter, subtract the base from perimeter and divide by 2.

When do you need to use the Pythagorean theorem in perimeter problems?

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Use the Pythagorean theorem when you have a right triangle and need to find the length of the hypotenuse or a leg before calculating perimeter. The formula a² + b² = c² helps you find the missing side length.

What are common mistakes students make when calculating triangle perimeter?

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Common mistakes include: forgetting to find missing side lengths first, confusing perimeter with area formulas, not recognizing triangle types (equilateral, isosceles), and making arithmetic errors when adding the three sides together.

How can I check if my triangle perimeter answer is reasonable?

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Verify your answer by ensuring: the perimeter is greater than any single side length, all side lengths are positive, and the triangle inequality holds (sum of any two sides must be greater than the third side).

What's the difference between finding perimeter of triangles vs other shapes?

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Triangles always have exactly three sides to add together. Circles use circumference formula (2πr), rectangles use 2(length + width), and squares use 4 × side length. Triangle perimeter is simply the sum of all three sides.

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