Explain Heron's formula.


Heron’s Formula:

In 60 A.D, a great mathematician named Heron replaced the value “h” in terms of a, b, & c so, that height is not required to calculate the area of the triangle.

The formula given by Heron about the area of a triangle is also known as Heron’s Formula.

It is given as:

Area of triangle $ = \sqrt{s (s-a) (s-b)(s-c)}$


Where a, b, & c are lengths of sides of a triangle and ‘s’ is called semi perimeter (half of the perimeter) of the triangle.

It is given as:-  


$s = \frac{a+b+c}{2}$



For example,

Consider a triangle of sides 6,8 and 10.

First, we need to find semi perimeter, s


$s = \frac{6+8+10}{2} = \frac{24}{2} = 12$

s=frac{6+8+10}{2}=frac{24}{2}=121displaystyle s= frac{6+8+10}{2} =frac{24}{2} =12

Substitute 's ' and a,b,c in the formula,


$A= \sqrt{12 (12-6)(12-8)(12-10)}$


$A= \sqrt{12 \times 6 \times 4 \times 2}$


$A= \sqrt{576}$


$A = 24$ sq units.



displaystyle A=sqrt{12( 12-6)( 12-8)( 12-10)} displaystyle A=sqrt{12times 6times 4times 2} displaystyle A=sqrt{576} displaystyle A= 24unit^{2}

Updated on: 10-Oct-2022

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