Scalene Triangle — Introduction
As far as geometry is concerned, a triangle signifies a two-dimensional closed figure having three sides with each corner forming an angle. Apparently there are three vertices and edges in a triangle. Based on their interior angles formed and sides, triangles can be classified into various types. Here, we will be broadly discussing the Scalene Triangle and its top properties. Unlike Equilateral and Isosceles, a scalene triangle is a unique type of triangle as all the three sides of a Scalene triangle are different from each other in terms of length.
Also, the measurement of all the three angles formed in a Scalene triangle are different from each other. Although these properties make Scalene triangles different from the other two triangles, the total sum of all the interior angles of a Scalene Triangle will always be equal to 180 degrees. There are a few striking factors when it comes to the Scalene Triangle.
Not only are its sides and interior angles different from each other, the other factor worth studying in a Scalene Triangle is that it neither has a line nor a point symmetry. There are however no such criterion regarding the angles of a Scalene Triangle, they can be acute, right or obtuse, but their sum total will always be equivalent to 180 degrees as mentioned earlier. We can calculate the area of the given Scalene Triangle with Heron’s formula.
Top Properties of a Scalene Triangle
The important properties of a scalene triangle which make it different from all other triangles are listed below –
1. Scalene Triangle is the only triangle where all the sides differ from each other.
2. Along with the sides the angles of a Scalene triangle too are different from each other.
3. The Scalene Triangle doesn’t have a line of symmetry.
4. Another important property of a Scalene Triangle is that it doesn’t have a point of symmetry.
5. There is nothing fixed regarding the angles inside a Scalene Triangle. They can be right angle, acute angle or obtuse angle.
6. If a situation arises where we can see that all the angles of the Scalene Triangle are Acute (less than 90 degrees) then the circumscribing circle will have its center inside the triangle.
7. In case of a Scalene Obtuse angled Triangle the circumcenter will always lie outside the triangle.
8. There is no fixed type of Scalene Triangle, it can be acute angled, obtuse angled or a right-angled triangle.
Scalene Triangle — More Information
Two main information regarding the Scalene Triangle that need to be noted are :-
1. Length of all the three sides of the Scalene Triangle.
2. Length of one side of the triangle along with the perpendicular distance the given side has from its opposite angle.
The formula for calculating the area of a Scalene triangle when information regarding Base and Height is (Area = 1/2 x base x height).
In case if all the three sides of a triangle is given, we use Heron’s formula for calculating the area of the Scalene Triangle and for this, we need to go through certain steps. The steps are as follows:-
1. We need to consider all the sides of a Scalene Triangle as X, Y, Z.
2. It is required to calculate the semi perimeters of the Scalene Triangle which is considered to be S using the formula (X+Y+Z/2)
Secondly, as we have calculated the Semi Perimeter (S) of the given triangle, we will be heading towards calculating the area of the given Scalene Triangle with Heron’s formula — Area = √{S(S-X)(S-Y)(S-Z)} sq. units
If the area of a Scalene Triangle is to be found where the height of the triangle is missing, the formula to calculate the area of the Triangle will be — (Area= ab/2).
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