Perimeter of Triangle

The perimeter of a triangle is necessarily defined as the sum total of the length of its boundary or the sides of a triangle. A triangle is a type of polygon that has 3 sides and this can be grouped into different types depending on the measure of its sides and the angles of the triangle. To measure the triangle or to measure the perimeter of triangle, there are different types of formulas and methods which help in calculating the perimeter of a triangle based on what type of triangle it is.

What Is The Formula For Calculating The Perimeter of a Triangle?

In order to calculate the perimeter or the summation of sides of a triangle, we simply need to add the lengths of the sides which will be given in the question. The basic and the general formula for calculating the perimeter of the triangle is as follows: Perimeter = sum of the three sides

Now we will know about all the formulae that give us the measurement of different types of triangles.

The Perimeter of a Scalene Triangle

A triangle having all its three sides of different lengths is a scalene triangle. The perimeter summed up for a scalene triangle can be estimated by finding the sum of all its unequal sides. Thus, the formula to estimate the perimeter of the scalene triangle is Perimeter equals to a + b + c, here “a”, “b”, and “c” represent the three different sides of the scalene triangle.

The Perimeter of an Isosceles Triangle

A triangle having two of its sides with equal length is typically an isosceles triangle. The perimeter of the isosceles triangle is to be calculated by estimating the sum of all its equal and the unequal sides. The formula that calculates the perimeter of an isosceles triangle is as follows:

The perimeter of an isosceles triangle = 2a + b, in this case

  • a is the sides of equal length
  • b is the third side

The Perimeter of an Equilateral Triangle

Triangle having all sides as equal and having an equal measurement is called the equilateral triangle. The formula to calculate the perimeter of the equilateral triangle is as follows:
The perimeter of an equilateral triangle is represented as 3 × a
‘a’ being the length of each side of the triangle.

The Perimeter of a Right-angled Triangle

A triangle that has one of its angles measuring 90º is known as the right-angle triangle. The perimeter of a right triangle is to be calculated by summing up all the given sides. The formula which assists us in calculating the perimeter of a right-angled triangle is:

Perimeter of a right triangle will be – P = a + b + c

Scalene Triangle

A scalene triangle is defined as a triangle that has all its three sides measuring a different length. In addition to this, all of its three angles measure a different measurement. Well, the different measurements will not affect the sum of these interior angles of a scalene triangle. Thus, the sum of the three interior angles always adds up to form 180 degrees, this satisfies the property of the scalene triangle known as the ‘angle-sum property’.

Properties of Scalene Triangle

Some of the basic properties of the scalene triangle are given as below:

  • The scalene triangle has three sides having different lengths.
  • Just like another triangle, a scalene triangle has three angles, but with different measurements.
  • A scalene triangle has parallel or equal sides and thus has no line of symmetry.
  • The interior angles of this right-angled triangle will be acute, obtuse, and also right-angled. Therefore, a scalene triangle can be of any angle.
  • When there is an acute scalene triangle, the center of the circumscribing circle will always lie inside the part of the triangle.

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