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How to Calculate the Perimeter of Different Types of Triangles?

A type of closed polygon that has three angles, three vertices, and three edges is known as a triangle. Triangles are one of the most basic geometric shapes that are introduced to children. There are several associated concepts of triangles, such as classification of triangles, area, and perimeter of scalene triangle that is important for children to study. In this article, we will see the different kinds of triangles and how to calculate the perimeter of each.

Classification of triangles

Triangles are classified into broadly two categories – length of sides and measure of angles.

Based on Sides

  • Equilateral Triangle: All the sides in this type of triangle are equal, and the interior angles are also of the same measure. Each angle at the vertex measures 60 degrees.
  • Isosceles Triangle: Only two sides out of three are of equal length. As the angles opposite to equal sides are equal hence, two angles are also of equivalent measure.
  • Scalene Triangle: When all three sides of a triangle are of unequal measure, it is termed a scalene triangle. Thus, the angles of such a triangle are also of unequal measure.

Based on Angles

  • Acute Triangle: All angles are less than right angles in this triangle. Equilateral triangles and scalene triangles can fall under this category.
  • Right Triangle: One angle has to measure 90 degrees. An isosceles triangle is a special case of this category. It can also include a scalene triangle.
  • Obtuse Triangle: One angle is greater than 90 degrees or is obtuse. A scalene or isosceles triangle can fall in this category.

The Perimeter of Equilateral Triangle

The perimeter of any triangle is defined as the total measure of all three sides of that triangle. We can calculate the perimeter of equilateral triangle by adding up the length of all the sides. The formula is given as:

Perimeter of Equilateral triangle = sum of all the three sides

However, as all three sides are equal in measure and we can modify the formula as given below. Suppose the side measures p units then, Perimeter = p + p + p = 3p.

The Perimeter of Isosceles Triangle

Say we have a triangle where two sides are of x units, and the third side is y units; then we get the perimeter of the triangle by the following formula,

Perimeter of Isosceles Triangle = x + x + y = 2x + y

The Perimeter of a Scalene Triangle

Let the measure of sides of a triangle be given by j, k, l, then the perimeter of a scalene triangle is given as: Perimeter of Scalene Triangle = j + k + l

Note: We can use the properties of triangles classified on the basis of the measure of angles to manipulate questions where we do not know the length of all sides to get an answer.

Example: Classify the triangle and find the perimeter if its sides measure 5 cm, 10 cm, and 5 cm.

Solution: As the two sides measure 5 cm, it implies that this triangle is isosceles. The formula for the perimeter of an isosceles triangle is given by

Perimeter = 2x + y = 2(5) + 10 = 20 cm.

Conclusion

There are many concepts associated with triangles, such as Pythagoras theorem, trigonometry, etc., Kids need to develop a good conceptual understanding of it, and hence, they should join an online educational institute such as Cuemath. At Cuemath, the certified experts ensure that children develop an in-depth knowledge of the subject while having an enjoyable learning experience. Students are sure to succeed with the proper guidance provided by Cuemath.

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