Perimeter of a Triangle Calculator

The triangle is an interesting and very common shape used in different industries as a base. Depending on the usage of the triangle, it is important to know its dimensions, area, and perimeter. But sometimes, it is not easy to calculate its perimeter if some values are missing. Our Perimeter of Triangle Calculator can help you with that. It uses basic formulas and finds the solution depending on your values.

Geometry is a very wide and interesting field, with different shapes and important values used in everyday life. For every shape, there are different calculators that can help you. If you are curious about the angles in the triangle, try our Triangle Angle Calculator. Or, if you want to find the perimeter of a rectangle, read more about the Perimeter of a Rectangle Calculator. If you want to know how to find the perimeter of a triangle, keep reading. Finally, math is an important subject in school after all.

Perimeter of a Triangle – What is?

As noted, the perimeter is an important calculation about the shape you have, but what is the perimeter of a triangle? The perimeter of a triangle shows the length or distance around that shape. One can understand it as calculating the length of a fence he needs to put around a kids’ playground in the shape of a triangle.

Perimeter of a Triangle – Formula

The basic equation for the perimeter of a triangle is very simple. First, you should add all the lengths of each triangle side. Since the triangle has three sides, the formula looks like this:

P=a+b+c 

Scalene, Isosceles, Equilateral, and Right Triangles – Perimeter

However, math can be trickier than this. There are different types of triangles, and for every one of them, we must use different formulas referring to the basic formula. The scalene triangle has three different sides with different angles between them. The formula for the perimeter is the basic one, adding all three values together as written in the equation above.

The isosceles triangle has two equal sides with two equal angles on the base. Then, its perimeter is:

P=2 \cdot a+b

The equilateral triangle has all three sides and angles the same. Thus, its perimeter is:

P=3\cdot a

The right triangle has one angle of 90°, and all sides can be different, or two can be the same. Therefore, to calculate the perimeter of a triangle, we have different methods, depending on the given values.

The first method is the simplest one when we have three lengths and the given angle. The formula is the basic one:

P=a+b+c

The second method is used when we know two sides and one angle. In this case, we use the Pythagorean theorem to find the missing side. The Pythagorean theorem says that the square of the hypotenuse is always equal to the sum of the squares of the other two sides. The hypotenuse is the length opposite the right angle, and it is the longest side. Therefore, the Pythagorean equation is c² = a² + b²

Having this in mind, we can find the missing side and include it in the basic equation for the perimeter of a triangle:

P = a + b +   \sqrt {a² + b² – 2 \times a \times b \times cos(γ)}

Another option for the perimeter of any triangle is when we have two angles and one side:

P = a + (a ÷ sin(β + γ)) × (sin(β) + sin(γ))

Perimeter of a Triangle Calculator – How to Use?

It is very simple to use a perimeter of a triangle calculator, just follow these steps:

1. You have to see what values are known and choose the right formula based on that.
2. You need to know which length represents which value.
3. Enter the values in the given boxes, and the solution will be ready in a second.

Practical Example

Let’s say you have a triangle with one right angle and two sides, where a=12, and b=16. We need to find value of c for P=a+b+c.

Using Pythagorean theorem we have c² = a² + b² , therefore c² = 144+256 . Then, we have that c is square root of 400, which is 20. From this, we can find the solution.

P=12+16+20 = 48.

Perimeter of a Triangle – Real Life Examples

A basketball coach wants to have a diagonal court line as a border between two competing teams during the practice. She considers a long rope and a few poles the best option for the installation. Before the next practice, she needs to calculate the length of the rope and buy the equipment. The length of a rope is a perimeter of a made triangle. Basketball court dimensions became triangle sides. The perimeter of a triangle calculator can help her. She needs to choose the type of a given triangle and enter the values into boxes.

Here, a = 15, b = 28, with a right angle between. Using this calculator, the coach gets the needed length of a rope, which is the perimeter of a triangle.

First, c² = a² + b² . Then, c² = \sqrt {225+784} = 31,76.

Then, since P=a+b+c, we include all values and get that P=74.76. Therefore, the coach needs 74,76 meters of rope.

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