Perimeter of a Triangle Calculator

Q: What's the formula used to find the perimeter of SAS triangle?

To find the perimeter of a triangle knowing two sides ( a and b ) and the angle between them ( γ ) or a SAS triangle, we use the law of cosines to find the third side and then the perimeter. As a result, we can use the following expression and the perimeter formula for a SAS triangle: perimeter_SAS = a + b + √(a 2 +b 2 - 2⋅a⋅b⋅cos(γ))

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Hanna (Hania) Pamuła holds a Ph.D. in Bioacoustics / Mechanical Engineering, obtained at AGH University of Science and Technology. She has participated in research work in labs in France and the UK and presented papers at several international conferences. Hania has a penchant for photography and graphic design. When not in the office, she’s probably traveling, hiking, or out in the field, watching birds and recording their calls. See full profile

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Adena Benn is a Guyanese teacher with a degree in computer science who is always reading and learning. She loves problem-solving, everything tech, and working with teenagers. She has a passion for education and is especially interested in how children learn and the teaching methods that best suit their learning styles. She grew up on a farm in Pomeroon, Guyana, where she worked alongside her parents and siblings. As such, she is just as comfortable growing plants as teaching in the classroom. In her early life, she also gained expertise as a seamstress, which she learned from her mother. By grade 9, she had already acquired her dressmaker's certificate. Today she uses her skills to design many items for her family. In her free time, Adena loves to read, take long walks, write children’s stories and poetry, travel, or spend time with her family. See full profile

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With our perimeter of a triangle calculator, you can easily calculate the perimeter of that figure. The tool has the basic formula implemented – the one assuming you know all three triangle sides. But that's not all - our calculator is better than the other ones you can find on the Internet because we've also implemented two other formulas for triangle perimeter, depending on the values you know. Isn't it awesome?

If you are still wondering how to find a triangle's perimeter or are curious about the formulas for a perimeter of a triangle behind this calculator, keep reading. Check out our other handy tools: triangle area calculator, right triangle calculator, and equilateral triangle calculator – these are a safe bet for your geometry problems.

What is the perimeter of a triangle?

The perimeter is a distance around the shape – in our case, around the triangle. You can think about it as a path surrounding this figure. In real-life problems, a perimeter of a triangle may be useful in making a fence around the triangular parcel, tying up a triangular box with ribbon, or estimating the lace needed for binding a triangular pennant. However, we guess that you will probably use it in your Maths class ;)

How to find the perimeter of the triangle? The formula for a perimeter of a triangle

The basic formula is uncomplicated. Just add up the lengths of all the sides of the triangle, and you will obtain the perimeter value:

Formula given three sides (SSS)

\quad\text{perimeter} = a+b+c

However, you don't always have three sides given. What can you do then? In these cases, other equations derived from trigonometry may be used, depending on what you know about the triangle:

perimeter of a triangle given 2 sides and angle between them

Two sides and the angle between them (SAS)

Use the law of cosines to find the third side and then the perimeter:

\begin{split}\text{peri}&\text{meter} = a+b\\ &+\sqrt{a^2\!+\!b^2\!-\!2\!\cdot \!a \!\cdot \!b\!\cdot\!\cos(\gamma) } \end{split}

perimeter of a triangle given 2 angles and side between them

Two angles and a side between them (ASA)

Use the law of sines to find the remaining two sides and then the perimeter:

\begin{split} \text{peri}&\text{meter} \!=\! a\!+\!a\frac{\sin(\beta)\!+\!\sin(\gamma)}{\sin(\beta+\gamma)} \end{split}

🙋 For an explanation of the law of sines and cosines, don't hesitate to visit our dedicated calculators: the law of cosines calculator and the law of sines calculator!

How to use our perimeter of a triangle calculator?

Let's take a practical application case as an example. Imagine that you want to make a small garden in your backyard and you want to calculate how much fence you need to enclose it.

Choose the formula, according to the data given. Assume that we know two sides of the triangle garden and the angle between them.
Enter the values into the proper boxes. Dimensions of our triangular garden are equal to $a= 8\ \text{ft}$ , $b = 6\ \text{ft}$ and the angle between them is $\gamma = 75\degree$ . Remember that you can choose the unit by clicking on its name.
Tadaaaam! The perimeter of a triangle calculator displays the solution in a blink of an eye! In our case, we need $22.67\ \text{ft}$ of fence.

We are sure that after this detailed explanation and example, you understood what the perimeter of a triangle is. Keep practicing!

FAQs

How do I find the perimeter of an SSS triangle?

To find the perimeter of a triangle knowing its three sides (SSS triangle), all you have to do is add the three known sides.

For example, the perimeter of a triangle with sides a = 3 cm, b = 2 cm and c = 4 cm can be calculated as follows:

perimeter_SSS = a + b+ c

perimeter_SSS = 3 cm + 2 cm + 4 cm

perimeter_SSS = 9 cm

What's the formula used to find the perimeter of SAS triangle?

To find the perimeter of a triangle knowing two sides (a and b) and the angle between them (γ) or a SAS triangle, we use the law of cosines to find the third side and then the perimeter. As a result, we can use the following expression and the perimeter formula for a SAS triangle:

perimeter_SAS = a + b + √(a² +b² - 2⋅a⋅b⋅cos(γ))

What's the formula used to find the perimeter of an ASA triangle?

To calculate the perimeter of a triangle knowing two angles (β and γ) and the side between them (a) or an ASA triangle, we use the law of sines to find the third side and then the perimeter. We express the perimeter formula for an ASA triangle as:

perimeter_ASA = a + a⋅(sin(β) + sin(γ)) / sin(β + γ)