Scalene Triangle: Definition, Properties, Formula, Examples

Scalene Triangle is defined as a type of triangle whose all sides and angles are unequal. It follows the angle sum property of the triangle.

Let’s discuss the properties, formula, and example problems on the Scalene triangle.

Scalene Triangle Definition

Scalene triangle is defined as a triangle whose all three sides are unequal and the unequal sides mean that its angles are also unequal.

It is to be noted that the angles in the scalene triangle follow the angle sum property of the triangle, i.e. the sum of all the different angles of the triangle is always 180°. In a scalene triangle, all the angles are also unequal.

The triangle added in the image below has unequal sides and unequal angles hence, it is a Scalene Triangle.

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• Triangles

Classification of Triangles

We can classify the triangles into various categories by comparing their sides and interior angles. Here is the basic classification of the triangle:

On the basis of the measure of interior angles, different types of triangles are,

• Acute Angle Triangle
• Right Angle Triangle
• Obtuse Angle Triangle

On the basis of the measure of the side of the triangles, they are categorized into three types, which include,

• Scalene Triangle
• Isosceles Triangle
• Equilateral Triangle

Scalene Triangle Types

Scalene triangles are based on the measure of their interior angles. They can be further classified into three categories that are,

• Acute-Angled Scalene Triangle
• Obtuse-Angled Scalene Triangle
• Right-Angled Scalene Triangle

Now let’s learn about them in detail.

Acute-Angled Scalene Triangle

An acute-angled scalene triangle is a scalene triangle in which all the interior angles of the triangle are acute angles. I

Obtuse-Angled Scalene Triangle

An obtuse-angled scalene triangle is a scalene triangle in which any one of the interior angles of the triangle is an obtuse angle(i.e. its measure is greater than 90°). The other two angles are acute angles.

Right-Angled Scalene Triangle

A right-angled scalene triangle is a scalene triangle in which any one of the interior angles of the triangle is a right angle (i.e. its measure is 90°). The other two angles are acute angles.

Scalene Triangle Properties

Key properties of a scalene triangle are,

• All three sides of a scalene triangle are not equal.
• No angle of the Scalene triangle is equal to one another.
• Interior angles of a scalene triangle can be either acute, obtuse, or right angle, but some of all its angle is 180 degrees.
• No line of Symmetry exists in the Scalene triangle

Difference between Scalene, Equilateral and Isosceles Triangles

The main differences between Scalene, Equilateral and Isosceles Triangles are tabulated below:

Equilateral Triangle	Isosceles Triangle	Scalene Triangle
Equilateral vs Isosceles vs. Scalene Triangles
In an Equilateral triangle, all three sides of a triangle are equal.	In an Isosceles triangle, any two sides of the triangle are equal.	In a Scalene triangle, no sides of a triangle are equal to each other.
All angles in an equilateral triangle are equal they measure 60 degrees each.	Angles opposite to equal sides of an Isosceles triangle are equal.	No two angles are equal in Scalene triangles.
The equilateral triangle is shown in the image added below,	The isosceles triangle is shown in the image added below,	The scalene triangle is shown in the image added below,

Read More On:

• Right Angle Formula
• Area of Triangle
• Area of Equilateral Triangle

Scalene Triangle Formula

A triangle with no two sides equal is called a scalene triangle. A scalene triangle has two major formulas

1. Perimeter of Scalene Triangle,
2. Area of Scalene Triangle

Let’s discuss these two formulas in detail.

Scalene Triangle Perimeter

Perimeter of any figure is the length of its total boundary. So, the perimeter of a scalene triangle is defined as the sum of all of its three sides.

From the above figure,

Perimeter = (a + b + c) units

Where a, b and c are the sides of the triangle.

Scalene Triangle Area

Area of any figure is the space enclosed inside its boundaries for the scalene triangle area is defined as the total square unit of space occupied by the Scalene triangle. Area of the scalene triangle depends upon its base and height of it. The image added below shows a scalene triangle with sides a, b and c and height h units.

When Base and Height are Given

When the base and the height of the scalene triangle is given then its area is calculated using the formula added below,

A = (1/2) × b × h sq. units

Where,

• b is the base and 
• h is the height (altitude) of the triangle.

When Sides of a Triangle are Given

If the lengths of all three sides of the scalene triangle are given instead of base and height, we calculate the area using Heron’s formula, which is given by,

A = √(s(s – a)(s – b)(s – c)) sq. units

Where,

• s denotes the semi-perimeter of the triangle, i.e, s = (a + b + c)/2, and
• a, b, and c denotes the sides of the triangle.

Scalene Triangle Examples

Let us solve some questions on scalene triangles and their properties.

Example 1: Find the perimeter of a scalene triangle with side lengths of 10 cm, 15 cm, and 6 cm.

Solution:

We have, 

• a = 10
• b = 15
• c = 6

Using the Perimeter Formula 

Perimeter (P) = (a + b + c)

⇒ P = (10 + 15 + 6)

⇒ P  = 31 cm

Thus, the required perimeter of the triangle is 31 cm.

Example 2: Find the length of the third side of a scalene triangle with two side lengths of 3 cm and 7 cm and a perimeter of 20 cm.

Solution:

We have, 

• a = 3
• b = 7
• P = 20

Using the Perimeter Formula 

Perimeter (P) = (a + b + c)

⇒ P = (a + b + c)

⇒ 20 = (3 + 7 + c)

⇒ 20 = 10 + c

⇒ c = 10 cm

Thus, the required length of third side of the triangle is 10 cm

Example 3: Find the area of a scalene triangle with side lengths of 8 cm, 6 cm, and 10 cm.

Solution:

We have, 

• a = 8
• b = 6
• c = 10

Semi-Perimeter (s) = (a + b + c)/2

⇒ s = (8 + 6 + 10)/2

⇒ s = 24/2

⇒ s = 12 cm

Using the Heron’s formula 

Area = √(s(s – a)(s – b)(s – c))

⇒ A = √(12(12 – 8)(12 – 6)(12 – 10))

⇒ A  = √(12(4)(6)(2))

⇒ A  = √576

⇒ A  = 24 sq. cm

Thus, the required area of the scalene triangle is 24 cm²

Example 4: Find the area of a scalene triangle whose base is 20 cm and altitude is 10 cm.

Solution:

We have, 

• b = 20 
• h = 10

Area of Scalene Triangle (A) = 1/2 × b × h

⇒ A  = 1/2 × 20 × 10

⇒ A = 100 sq. cm

Thus, the area of the given scalene triangle is 100 sq. cm.

Scalene Triangle Practice Questions

Here is a list of questions on scalene triangle for your practice.

1: Find Area of a Scalene Triangle with base is 24 cm and altitude is 16 cm.

2. Find the area of Scalene Triangle with sides, 3 cm, 4 cm and 5 cm.

3: Find the perimeter of the scalene triangle with sides, 10 cm, 11 cm, 13, cm.

4: Check wether they are Scalene Triangle or not if the sides are,

• 12 cm, 13, 14 cm
• 16 cm, 18 cm, 22 cm
• 8 cm, 12 cm, 8 cm

Scalene Triangle- FAQs

1. What is Scalene Triangle in Geometry?

Scalene triangles are triangles with all three sides unequal, i.e. in a scalene triangle, no two sides are equal. Also, all the angles in the scalene triangles are unequal.

2. Can Scalene Triangles be Obtuse?

Yes, a scalene triangle can be an obtuse-angled triangle. For an obtuse-angled triangle, any one angle is greater than 90° and the other two angles are less than 90° such that the total sum is 180° which is possible in a scalene triangle.

3. What are Properties of Scalene Triangle?

Various properties of Scalene Triangle are,

• In a scalene triangle, all sides and all angles are unequal. 
• Scalene triangle has no line of symmetry. 
• For a scalene triangle, interior angles can be acute, obtuse, or right-angle.

4. How to find the Area of Scalene Triangle?

The area of scalene triangle can be calculated by the following formula :

• Area of Scalene Triangle (A) = 1/2 × b × h

where,

• b is the base of triangle
• h is the height of triangle

5. What is the perimeter formula of Scalene Triangle?

The perimeter formula of the scalene triangle is,

• Perimeter of Scalene Triangle (P) = a + b + h

where,

• a, b, c are sides of triangle
• b is the base of triangle
• h is the height of triangle

6. Does the angle sum property hold true for scalene triangle?

Yes, the angle sum property holds true in the scalene triangle. According to the angle sum property of the triangle sum of all the angles of the triangle is 180 degrees. And the sum of all the interior angles of the triangle is 180 degrees.

7. What is Right Scalene Triangle?

A scalene triangle with one right angle(i.e. angle with a measure of 90 degrees) is called a right scalene triangle. The other two angles of this triangle are acute angles.

8. What is Acute Scalene Triangle?

A scalene triangle with all three interior angles as acute angles is called the acute scalene triangle, all these three angles in the acute scalene triangle are unequal.

9. What is Scalene vs Obtuse Triangle?

In a scalene triangle (types of triangle on the basis of side) all sides of triangle are unequal where as, in a obtuse angle triangle (types of triangle on the basis of side) an angle of the triangle must be obtuse. A scale triangle can be an obtuse angle triangle and vice-versa.