To classify a triangle by its sides means that we look at the lengths of sides and make a determination as to whether it is of the type as Equilateral, Isosceles, and Scalene. Also, for an equilateral triangle, all three side lengths must be exactly the same. In the scalene triangles, all sides will be of different lengths. This article will deal with the Scalene triangle formula with examples. Let us learn it!

## What is the Scalene Triangle?

Classification of the triangle is as simple as comparing its sides. If all three sides are having the same length, then it is an equilateral triangle. Similarly, if only two sides have the same length then it is an isosceles triangle. And if there are no sides that have the same length then it is termed as the Scalene triangle.

Therefore, Scalene triangles are triangles with each side with a different length. They are unusual in the way, which they are not. Most triangles drawn at random will be of this kind. The interior angles of a scalene triangle are all also different. Its converse is also true.

Thus, if a triangle has 3 unequal sides and also the angles of the triangle are different then it will be definitely a Scalene triangle. Its some notable properties are the triangle with 3 unequal sides, 3 unequal angle measures and having no line of symmetry. It has no point symmetry at all. The angles in the triangle may be an acute, obtuse or right angle.

## The Formula for Scalene Triangle

Some useful scalene triangle formula are as follows:

- Area of Triangle = \(\frac{1}{2} \times b \times h\), where b is the base and h is the height.
- The formula for Perimeter of any Triangle is, P = a+ b + c where a, b, c are the length of the sides
- When all three sides are given then the area of the triangle will be, \(A = \sqrt {[s \times (s-a) \times (s-b) \times (s-c)]}\), where s is the semi-perimeter of the triangle. Also, \(0s = \frac {1}{2} (a+b+c)\)

## Solved Examples for Scalene Triangle Formula

Q.1: If the base of a triangle is 6 and height is 12cm, Find the area of this type of scalene triangle.

Solution: Given in the problem,

b = 6 cm

h = 12 cm

thus are of this triangle will be,

\(Area = \frac{1}{2} \times b \times h\)

\(Area = \frac{1}{2} \times 6 \times 12\)

= \(36 cm^{2}\)

Q.2: Find the perimeter of a triangle whose sides are of the lengths 6 cm, 8 cm and 6 cm.

Solution: Given length of sides are,

a = 6 cm

b = 8 cm

c = 6 cm

Therefore, perimeter of this triangle will be,

= a + b + c

= 6 + 8 + 6

= 20 cm

Q.3: Find the area of the scalene triangle ABC with the sides 8cm, 6cm and 4cm.

Solution:

a= 8 cm

b = 6 cm

c = 4 cm

Also ,

\(s = \frac {1}{2} (a+b+c)\)

s = 9 cm

Now formula for area is,

\(Area = \sqrt {[s \times (s-a) \times (s-b) \times (s-c)]}\)

\(Area = \sqrt {[9 \times (9-8) \times (9-6) \times (9-4)]}\)

\(= \sqrt { 135}\)

\(= 11.6 cm^{2}\)

Therefore, the area of the scalene triangle will be 11.6 square cm.

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