How to calculate the area and perimeter of a scalene triangle?

A triangle is a closed two-dimensional geometrical figure which has three sides and three angles. A triangle can be classified based on its side or its angles. There are three types of triangles based on their sides. They are (1) EquilateralTriangle, (2) Isosceles Triangle, (3) Scalene Triangle. In Equilateral triangles, the length of all the sides is the same. In the Isosceles triangle, the two sides are the same in length. A Scalene triangle is a triangle that has all its sides of different lengths. Here in this article, we are going to discuss the Scalene triangle and the formulas for calculating the area and perimeter of it.

Definition: A scalene triangle is that type of triangle in which all three sides are in different lengths, and all the three angles are of different measurement. The sum of all the three interior angles of a scalene triangle is always equal to 180 degrees.

Some important properties of the scalene triangle are as follows:

  • It has no equal sides in length
  • It has no equal angles.
  • It has no line of symmetry.
  • The angle inside the scalene triangle can be an acute, obtuse, or right angle.
  • In a scalene obtuse triangle, the circumcentrewill lies outside the triangle.
  • A scalene triangle can be an obtuse-angled, acute-angled, or right-angled triangle.

Formulas to calculate the area of a Scalene Triangle: If you want to calculate the area of the Scalene triangle, you need to make a couple of measurements. If you can measure the length of one side and the perpendicular distance of that side to the opposing angle, you can easily calculate the area. If you know the length of the three sides, it is also possible to calculate the area. If you can determine the value of one angle and the length of two sides you will be able to calculate its area. There are some formulas to calculate the area of the triangle as well as the scalene triangle.

The general formula for finding area: 

Area=1/2× base × height

Area oh scalene triangle formula when any side considered as base ‘b’ and height ‘h’, this formula is used. It possible to draw a rectangle around it that uses one of the sides as its base and just touch the apex of the third angle. The length of this rectangle equals the length of the side of the triangle that forms the base. Its width is equal to the perpendicular distance from the base of the apex, which is called height of the triangle.

If all the length of three sides given, then the area of a triangle is calculated by Heron’s formula.

Heron’s formula: Heron’s formula was first used by Heron of Alexandria. It is used to find area for different types of triangle. When the length of all the sides of triangle is given Heron’ a formula is used to find out the area of the triangle. It solely depends on the length of all the sides othef triangle. AS per Heron’s formula the value of the area of any triangle having length a, b, c, perimeter of the triangle, p, and semi- perimeter of the triangle, s, is determined using the below- given formula-

Area of triangle ABC =√s(s-a) (s-b) (s-c),

Where s= Perimeter/2=(a+b+c)/2’

For more queries about Heron’s formula, you may go through the Cuemath website.

The law of Cosines: Mark the three angles of a triangle as A,B, C and the length of the sides as a, b, c. Side a is opposite to the angle A, side b is opposite to the angle B and side c is opposite to the angle C. If you know one side of the angle -for example, angle C and the two sides that form it _in this case, a and b, -you can calculate the length of the third side using this formula:

c2= a2+b2- 2ab cos(C)

Once you can calculate the value of c, you can calculate the area using Heron’s formula.

The perimeter of a Scalene Triangle:

The perimeter of a triangle is equal to the sum of the length of sides of a triangle and it is given as:

perimeter= a+ b+ c units 

You may download the Cuemath learning app and learn and all the Math topics. This app you help you with more knowledge about all the areas of math.


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