What is Heron's formula

Heron's formula: Definition, formulas and examples

 Table of contents

1. Definition of heron's formula:
2. Heron’s formula
3.Area Removal Process:
4.Examples:

1. Definition of heron's formula:

 Heron's formula is used in geometry to find the area of ​​a triangle.  If we know the measurement of three sides of a triangle, then we can find the area of ​​that triangle using this formula.

 When we use this formula, we do not need to find the angle of the triangle to find the area of ​​that triangle and this makes it very easy.  To use this formula, we just have to measure all three sides and we can find the area of ​​that triangle.

 As you can see in the figure above, there is a triangle ABC.  If we know the measure of its three sides, then we can find the area of ​​this triangle by placing it in the Heron formula.

2. Heron’s formula

 According to Heron's formula, placing the measurement of the three sides of the above triangle in the formula will bring its area.

 Half Dimension s = (a + b + c) / 2

 Area of ​​ triangle = √ [s (s-a) (s-b) (s-c)]

3. Area Removal Process:

 A triangle ABC whose area we want to find is the first measure we need to measure its three sides.  This is often given in question.

 After getting the measurement of the three sides, we have to find the semicircle of this triangle.  We mark half the perimeter with s.  We deduce the semi-perimeter of a triangle as follows:

 s = (a + b + c) / 2

 By extracting half the perimeter, we get the value of s.  We have to put the value of s in the remaining formula.  The following formula is:

 = √ [s (s-a) (s-b) (s-c)]

 When we put the measurement of s and the sides in this formula and solve it further, in the last we will have the area of ​​this triangle.

4. Examples:

 Let us now learn the area of ​​triangles from this formula:

 Example 1: The measurement of the three sides of a triangle is as follows: 3 cm, 4 cm and 5 cm Find the area of ​​this triangle with the formula of Heron.

 Solution: As you can see above, here we have been given a triangle and we know the measurement of its three arms.  Un we have to find the area of ​​this triangle with the formula of Heron.

 a = 3 cm, b = 4 cm and c =6cm

 First of all, we will find the semi-perimeter of this triangle by measuring the sides.

 s = (a + b + c) / 2

 s = (3 + 4 +6) / 2

 s = 13/2 =6.5 cm

 s = 6.5 cm

 Now, as you can see, we have got the semi-perimeter of this triangle, so now we go ahead and now, taking the value of the half-perimeter in the formula, let's find out the area of ​​this triangle.

 Area of ​​a triangle = √ [s (s-a) (s-b) (s-c)]

 = 385/ 16

 As you saw, we removed the area of ​​a triangle using the formula of Heron and following this procedure.  Similarly, we can also find the area of ​​another triangle.  Its only condition is that we should know the measurement of the three sides of the given triangle.