RD Sharma Solutions for Class 9 Maths Chapter 12 - Heron's Formula

What is Heron's Formula?

The Heron Formula is used to determine the area of ​​a triangle where the length of all their sides is given or the location of the quadrilaterals. We also know it as a Hero formula. This location finding formula does not depend on the angles of the triangle. It depends only on the length of all the sides of the triangle. It contains the word "s" known as the semi-perimeter, which is obtained by dividing the triangle into a triangle. Similarly, the concept of location acquisition is expanded to determine the location of quadrilaterals.

Heron of Alexandria was the first to give Heron's Formula. It is used to locate different types of triangles such as equal triangles, isosceles, be scalene triangles, or quadrilaterals. In this article, we will find out how to determine the area of ​​a triangle or quadrilateral using the Heron formula using examples. Stay tuned to learn more about it.

History of Heron Formula

Heron's formula was written by Heron of Alexandria in 60 CE . Heron was a Greek Engineer and mathematician who calculated the area of ​​a triangle using only the sides of its sides and extended it to calculate quadrilateral areas. He used this formula to prove trigonometric rules such as cosine Laws or cotangent Laws.

Heron’s Formula Definition

According to the Heron Formula, the area value of any triangle with a length, a, b, c, the circumference of a triangle, P, and a fraction of a triangle as s is determined using the formula given below:

Area of the triangle ABC = √s (s-a) (s-b) (s-c), where s = Perimeter / 2 = (a + b + c) / 2

Example: Find the area of ​​a triangle which is 5 units long, 6 units, and 9 units respectively.

Solution: we know that, a = 5 units, b = 6 units and c = 9 units

Thus, Semi-perimeter, s = (a + b + c) / 2 = (5 + 6 + 9) / 2 = 10 units

Location of triangle = √ (s (s-a) (s-b) (s-c)) = √ (10 (10-5) (10-6) (10-9))

⇒ The position of the triangle = √ (10 × 5 × 4 × 1) = √200 = 14.142 unit2

∴ The area of ​​the triangle is 14.142 unit2

How Do You Get a Location Using Heron Formula?

The steps to determine a Location using the Heron Formula are:

• Step 1: To Find the perimeter of the given triangle.

• Step 2: Find the semi-perimeter by dividing the perimeter.

• Step 3: Find the location of the triangle using the Heron Formula which is  √ (s (s) - a) (s - b) (s - c)).

• Step 4: Once the value is fixed, write the unit at the end (for example, m², cm², or in 2).

Heron Formula Applications

Heron Formula has many applications of course:

• It can be used to determine the location of different types of triangles if the lengths of their different sides are given.

• It can be used to determine the quadrilateral position if the length of all its sides is given.

Topics Related to Heron Formula

• Heron's Formula Calculator

• Triangle location

• Location of Triangle Calculator

• Scalene Triangle location

• Quadrilateral location

• Quadrilateral calculator location