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The perimeter of a triangle refers to the total length of its three sides. In geometry, finding the perimeter is a fundamental concept and an important skill. It is crucial for various applications, such as constructing objects, calculating fence requirements, and determining the distance to travel around a triangular region. In order to find the perimeter of a triangle, one must understand its basic properties and employ specific formulas. This guide will provide a step-by-step explanation of the process involved in finding the perimeter of a triangle, along with examples and illustrations to enhance comprehension. Whether you are a student learning geometry or an individual in need of practical measurements, this topic will equip you with the necessary knowledge and tools to confidently find the perimeter of any triangle.
This article was co-written by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math teacher at City University of San Francisco and previously worked in the math department of Saint Louis University. She has taught math at the elementary, middle, high, and college levels. She holds a master’s degree in education from Saint Louis University, majoring in management and supervision in education.
This article has been viewed 16,703 times.
Finding the perimeter of a triangle means finding the length around that triangle. [1] XResearch Source The simplest way to find the perimeter of a triangle is to add up the lengths of all the sides. However, if you don’t know the lengths of the sides, you have to find them first. At the beginning, this article will show you how to find the perimeter of a triangle knowing the lengths of its three sides – that’s the easiest and most common way. Next, the article will teach you how to find the perimeter of a right triangle when only the lengths of two sides are known, and finally find the perimeter of any triangle knowing the lengths of the two sides and the angle between those two sides. (“Side-angle-triangle”) using the Cosine theorem.
Steps
Find the perimeter when the lengths of the three sides of a triangle are known
![Image titled Find the Perimeter of a Triangle Step 1](https://www.wikihow.com/images/thumb/3/38/Find-the-Perimeter-of-a-Triangle-Step-1-Version-2.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-1-Version-2.jpg)
- Simply put, to find the perimeter of a triangle, we simply add the lengths of their three sides.
![Image titled Find the Perimeter of a Triangle Step 2](https://www.wikihow.com/images/thumb/b/bb/Find-the-Perimeter-of-a-Triangle-Step-2-Version-2.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-2-Version-2.jpg)
- The triangle in this particular example is called an equilateral triangle, because all three of its sides are of equal length. Remember, though, that the formula for perimeter is the same for all types of triangles.
![Image titled Find the Perimeter of a Triangle Step 3](https://www.wikihow.com/images/thumb/8/85/Find-the-Perimeter-of-a-Triangle-Step-3-Version-2.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-3-Version-2.jpg)
- In another example, for a = 4 , b = 3 , and c=5 , the perimeter of that triangle would be: P = 3 + 4 + 5 , which is 12 .
![Image titled Find the Perimeter of a Triangle Step 4](https://www.wikihow.com/images/thumb/e/e3/Find-the-Perimeter-of-a-Triangle-Step-4-Version-2.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-4-Version-2.jpg)
- In the above example, the length of each side is 5 cm, so the exact value of the circumference is 15 cm.
Find the perimeter of a right triangle when two of its sides are known
![Image titled Find the Perimeter of a Triangle Step 5](https://www.wikihow.com/images/thumb/3/38/Find-the-Perimeter-of-a-Triangle-Step-5-Version-2.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-5-Version-2.jpg)
![Image titled Find the Perimeter of a Triangle Step 6](https://www.wikihow.com/images/thumb/1/14/Find-the-Perimeter-of-a-Triangle-Step-6-Version-2.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-6-Version-2.jpg)
![Image titled Find the Perimeter of a Triangle Step 7](https://www.wikihow.com/images/thumb/9/9c/Find-the-Perimeter-of-a-Triangle-Step-7.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-7.jpg)
![Image titled Find the Perimeter of a Triangle Step 8](https://www.wikihow.com/images/thumb/6/66/Find-the-Perimeter-of-a-Triangle-Step-8.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-8.jpg)
- For example, if you know that side a = 3 and side b = 4 , then substitute these values into the formula like this: 3 2 + 4 2 = c 2 .
- If the length of the side a = 6 , and the hypotenuse c = 10 , then the equation would be set up as follows: 6 2 + b 2 = 10 2 .
![Image titled Find the Perimeter of a Triangle Step 9](https://www.wikihow.com/images/thumb/5/50/Find-the-Perimeter-of-a-Triangle-Step-9.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-9.jpg)
- In the first example, we squared the values in 3 2 + 4 2 = c 2 to get 25= c 2 . Next, take the square root of 25 to get c = 5 .
- In the second example, we square the values in 6 2 + b 2 = 10 2 to get 36 + b 2 = 100 . Subtract both sides by 36 to get b 2 = 64 , then take the square root of 64 to get b = 8 .
![Image titled Find the Perimeter of a Triangle Step 10](https://www.wikihow.com/images/thumb/a/a3/Find-the-Perimeter-of-a-Triangle-Step-10.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-10.jpg)
- In the first example: P = 3 + 4 + 5, which is 12 .
- In the second example: P = 6 + 8 + 10, which is 24 .
Already have the perimeter but lack the length of an edge? Subtract the sum of the other two sides from the perimeter. The result will be the length of the missing edge.
Find the perimeter of a side-angled triangle using the Cosine theorem
![Image titled Find the Perimeter of a Triangle Step 11](https://www.wikihow.com/images/thumb/7/7b/Find-the-Perimeter-of-a-Triangle-Step-11.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-11.jpg)
![Image titled Find the Perimeter of a Triangle Step 12](https://www.wikihow.com/images/thumb/9/93/Find-the-Perimeter-of-a-Triangle-Step-12.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-12.jpg)
- For example, imagine a triangle with sides 10 and 12 respectively, and the angle between them measures 97°. We will assign variables like this: a = 10 , b = 12 , C = 97°.
![Image titled Find the Perimeter of a Triangle Step 13](https://www.wikihow.com/images/thumb/7/78/Find-the-Perimeter-of-a-Triangle-Step-13.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-13.jpg)
- c 2 = 10 2 + 12 2 – 2 × 10 × 12 × cos (97) .
- c 2 = 100 + 144 – (240 × -0.12187) (Round cosine to five decimal places).
- c 2 = 244 – (-29.25)
- c 2 = 244 + 29.25 (Bring a minus sign because cos (C) is negative!)
- c 2 = 273.25
- c = 16.53
![Image titled Find the Perimeter of a Triangle Step 14](https://www.wikihow.com/images/thumb/6/66/Find-the-Perimeter-of-a-Triangle-Step-14.jpg/v4-728px-Find-the-Perimeter-of-a-Triangle-Step-14.jpg)
- In this example: 10 + 12 + 16.53 = 38.53 , which is the perimeter of the triangle to find!
This article was co-written by Grace Imson, MA. Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math teacher at City University of San Francisco and previously worked in the math department of Saint Louis University. She has taught math at the elementary, middle, high, and college levels. She holds a master’s degree in education from Saint Louis University, majoring in management and supervision in education.
This article has been viewed 16,703 times.
Finding the perimeter of a triangle means finding the length around that triangle. [1] XResearch Source The simplest way to find the perimeter of a triangle is to add up the lengths of all the sides. However, if you don’t know the lengths of the sides, you have to find them first. At the beginning, this article will show you how to find the perimeter of a triangle knowing the lengths of its three sides – that’s the easiest and most common way. Next, the article will teach you how to find the perimeter of a right triangle when only the lengths of two sides are known, and finally find the perimeter of any triangle knowing the lengths of the two sides and the angle between those two sides. (“Side-angle-triangle”) using the Cosine theorem.
In conclusion, finding the perimeter of a triangle is a relatively simple process. It involves adding up the lengths of all three sides of the triangle. By using the given side lengths or employing the Pythagorean theorem to find missing side lengths, one can easily determine the perimeter. Additionally, it is important to remember that the perimeter is a measure of the total distance around the triangle and is always expressed in units of length. By following these steps and utilizing the necessary formulas, anyone can accurately find the perimeter of a triangle.
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