Heron’s Formula: Calculating Area of Triangles

by Yuvi K - December 21, 2023

Heron’s Formula: Understanding the Calculation of Area of Triangles

The concept of triangles has been a part of mathematics for thousands of years. From the time of Euclid, the great mathematician, we have established ways to calculate the area of a triangle using three sides only – what is now known as Heron’s Formula. In this article, we shall explore this formula to understand how it works and how it is used to calculate the area of triangles.

What is A Triangle? ( क्या है त्रिभुज?)

A triangle is a two-dimensional figure that is formed by three line segments or three points. It is a polygon that has three angles and three sides. The sum of all the angles in a triangle is always equal to 180 degrees. Triangles can be classified into different types depending on the lengths of the sides and the angles formed by the vertices.

Heron’s Formula: Understanding The Definition( Heron’s Formula: परिभाषा को समझने

Heron’s formula is an equation that is used to find the area of a triangle given the lengths of its three sides. It is named after Hero of Alexandria, who discovered it. The formula is written as follows:

A = √ s (s − a) (s − b) (s − c)

Here, A is the area of the triangle, s is half of the perimeter of the triangle, and a, b and c are the lengths of the three sides of the triangle.

Solving Heron’s Formula: Steps for Calculating Area (Heron Formula का समाधान : क्षेत्रफल की गणना के लिए चरण )

Before attempting the formula, you need to have the lengths of all three sides of the triangle. It is also advisable to measure the sides correctly, because incorrect measurements can lead to incorrect conclusions at the end.

Once you have the measurements, taking the following steps will help you calculate the area of the triangle using the Heron’s formula:

Find the perimeter (क्षेत्रफल के लिए प्रमाण ढूंढें)The first step is to calculate the perimeter of the triangle. The perimeter is the total length of all the sides of the triangle combined. To calculate the perimeter, add up all the lengths of the three sides.
Calculate Semi-Perimeter ( अर्ध प्रमाण की गणना करें)The next step is to calculate the semi-perimeter of the triangle. This is half of the perimeter of the triangle. To calculate the semi-perimeter, divide the perimeter by two.
Calculate the Area ( क्षेत्रफल की गणना करें ) Finally, the last step is to calculate the actual area of the triangle. To do this, substitute the perimeter and the lengths of the three sides into the Heron’s formula given above and then find the square root of the result. The square root of the result will give you the area of your triangle.

Example: Applying Heron’s Formula ( उदाहरण : Heron फार्मूला का प्रयोग करना

Consider a triangle with side lengths as 6 cm, 8 cm and 10 cm.

Find the perimeter (क्षेत्रफल के लिए प्रमाण ढूंढें):
The first step is to calculate the perimeter of the triangle. Adding the three side lengths, we get that the perimeter is 6+8+10 = 24 cm.
Calculate Semi-Perimeter ( अर्ध प्रमाण की गणना करें):
The next step is to calculate the semi-perimeter. Dividing the perimeter by 2, we get that the semi-perimeter is 12 cm.
Calculate the Area ( क्षेत्रफल की गणना करें ):
The last step is to calculate the area of the triangle. Substituting the values into the Heron’s formula, we get

A = √ s (s – a) (s – b) (s – c)

A = √ 12 x (12 – 6) x (12 – 8) x (12 – 10)

A = √ 12 x 6 x 4 x 2

A = √ 576

A = 24

Therefore, the area of the triangle with sides 6, 8 and 10 cm is 24 square centimeters.

Conclusion

In conclusion, Heron’s formula is an important and useful tool for finding the area of a triangle given the lengths of its three sides. The formula is simple and easy to use, and can be used to calculate the area of any triangle provided the lengths of the three sides are known.