What is the Area and Perimeter of a Scalene Triangle?

What is the Area and Perimeter of a Scalene Triangle?

A triangle can be defined as a polygon with three sides and three vertices that are joined end to end to form a closed figure. When a student is introduced to triangles, he starts learning about the different types of triangles such as equilateral, right, scalene triangles, etc. They also learn about the different properties associated with them and certain computations, such as finding the area of scalene triangle.

In this article, we will learn more about a scalene triangle and how to find its perimeter and area. 

What is a Scalene Triangle?

When we categorize triangles on the basis of sides, we have three types, namely, equilateral triangle, isosceles triangle, and scalene triangle. Equilateral triangles have all sides equal, while isosceles triangles have two sides equal. A scalene triangle is one where all sides are unequal. This means that all the sides of a scalene triangle have a different length. A real-life example of a scalene triangle could be the sail of a sailboat. The sail is in the shape of a triangle with all sides of unequal length. 

Properties of a Scalene triangle 

  • All angles are unequal 
  • A scalene triangle does not have a line of symmetry and cannot be divided into two equal parts 
  • The angle opposite to the shortest side is the smallest and vice versa

Area of a Scalene triangle

The area of a triangle can be defined as the region that is enclosed by the three sides of that triangle. There are several methods that can be used to calculate the area of triangle with 3 sides of unequal lengths, as listed below. 

  1. Heron’s Formula

When the length of all three sides is known, this formula can be applied. Say we have a triangle with side lengths given by t, v, and w. Then the Heron’s formula is given by:

A = s (s – t) (s – v) (s – w) where s stands for the semi – perimeter of the triangle and is given by:

s = ( t + v + w) / 2

  1. Base and Height Formula

If we know the length of any one side and its corresponding height, this formula can be used. Say we have a triangle with side length t and height u. The base and height formula is applied as:

A = ½ (base) (height) 

A = ½ (t) (u) 

  1. Area without height

Suppose we know one angle of a triangle (say S) and the lengths of two sides say (t and v), we can find the area by the following formula. 

A = (t*v)/2 * sinS

Perimeter of a Scalene triangle 

The perimeter of a triangle is given by summing up the lengths of all three sides or boundaries. Suppose we have a triangle with side lengths t, v, and w, then the perimeter is given by 

Perimeter = sum of all sides

      = t + v + w 


Triangles form an important topic of Geometry. If young minds do not have a clear understanding of how to solve problems based on triangles, their foundation for Geometry will be shaky. Thus, it is best to approach a reliable institution for this purpose. Cuemath is a fantastic online educational platform that provides quality education to students. The certified tutors use resources such as online worksheets, puzzles, interactive games, etc., to explain concepts to kids. This results in more effective assimilation of knowledge. They combine fun with studies and help children learn faster. Start your journey of learning triangles with Cuemath today!  



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