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A triangle is a polygon with three sides and three angles. One fundamental property of any shape is its perimeter, which is the total length of all its sides. In the case of a triangle, finding its perimeter can be a relatively simple process, as it requires adding up the lengths of the three sides. However, the challenge lies in determining the lengths of these sides, which can be accomplished using various techniques and formulas depending on the information available. This article will explore the different methods and formulas used to find the perimeter of a triangle, providing step-by-step explanations and examples to ensure a comprehensive understanding of this essential geometric concept. Whether you are a student learning basic geometry or an enthusiast exploring the intricacies of polygons, understanding how to find the perimeter of a triangle is an essential skill that will serve as a foundation for further mathematical reasoning and problem-solving.
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] X Research 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
- Simply put, to find the perimeter of a triangle, we simply add the lengths of their three sides.
- 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.
- 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 .
- 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
- 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 .
- 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 .
- 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
- 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°.
- 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
- 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] X Research 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 simple yet important concept in geometry. By adding the lengths of all three sides of the triangle, we can determine its total perimeter. This method allows us to quantify the distance around the triangle, providing valuable information for various applications such as construction, engineering, and design. By understanding the formula and mastering the calculation of the perimeter, we can further explore the geometric properties and relationships within triangles. As a fundamental concept in mathematics, the ability to find the perimeter of a triangle is a skill that every student should acquire.
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