How do you calculate the circumference of a triangle?

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It is very easy to calculate the circumference of a triangle. All you have to do is re-understand how to define the perimeter and what a triangle is. Then there is no question of how to calculate it.

How to calculate the girth

Think for a moment about how to calculate a circumference in general before moving on to that of the triangle:

  • Perimeter is the sum of the length of all lines that delimit an area. Seen figuratively you can imagine a cord with which you span this area, similar to a fence around a piece of land. This length is then the circumference of an area.
  • So all you have to do is add the length of all sides of a surface. Depending on the task at hand, this length of this route must first be calculated.
  • Since a triangle consists of 3 side lines (segments), which are usually referred to as a, b and c, this means for the circumference U = a + b + c. Note that it is special Triangles where the routes are designated differently.

Determine the perimeter of a special triangle

  • In an isosceles triangle, the base side c is usually referred to as g and the two legs are also referred to as s. But it also happens that in exercises it is said that the legs are called a. In this case, the triangle is bounded by the segments a, which occur twice, and the segment g. So for the circumference of the triangle you have to have 2 times the length of a (or s) and add the length of the segment g (or c) add up. U = 2a + c = 2a + g = 2s + g, depending on how the routes are named in the exercise.
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  • If it is an equilateral triangle, then all three lines that delimit the triangle are of the same length. If you want to calculate the circumference of the triangle, you calculate 3 times this distance.
  • How to calculate the perimeter of a right triangle is also easy. All you have to do is add the length of the three sides. But here, in connection with the Pythagorean theorem c2= a2+ b2 refrains from naming all 3 side lengths in exercises. So you must first calculate the length of the missing side using the above formula before you add up the side lengths.

Read the assignment carefully and make a sketch so that you can better recognize which pages appear twice or how to apply the Pythagorean theorem.

How to calculate the side length of a triangle

  • The circumference is always the sum of the 3 sides, but often the lengths of the sides are not given to you. According to the congruence theorems, you can too angle and only part of the pages will be given. You either have to construct the triangle and measure the lengths of the sides or, if you already had trigonometry, calculate it. Here is a compilation of the solutions:
  • According to the congruence theorem WSW: You know 2 angles and the length of the side between them. In this case, calculate the missing angle using the sum of the angles 180 ° = alpha + beta + gamma, and then use the sine theorem a / sin alpha = .b / sin beta = c / sin gamma to calculate the side lengths. Example: Given is alpha = 30 °, c = 5 cm and beta = 45 °. Gamma is then 105 ° b = (c sin beta) / sin gamma = 5 sin 45 ° / sin 105 ° = 3.6 cm. Then calculate a = (c sin alpha) / are gamma = 2.6 cm. U = 5 + 3.6 + 2.6 = 11.2 cm. So the perimeter of the triangle n is calculated in the case.
  • SSW sentence: How you calculate the circumference in this case is certainly also clear. Assuming you have given c = 5 cm, a = 2.6 cm and gamma = 105 °, then, according to the law of sines, first calculate the angle beta and then the length of the missing segment b. You get w = 3.6 and U = 11.2 cm.
  • SWS Sentence: If you know two sides and the angle between them, you have to find the missing side calculate according to the cosine law, as in the example a = 2.6 cm, c = 5 cm and beta = 45 ° you have to use the sentence b2 = a2 + c2 - Calculate 2 a c cos beta.

How to calculate the perimeter of a triangle is easy, but it can be difficult to calculate the length of the sides you need for the perimeter.

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