Consider a triangle ABC having its all three sides with known values, i.e a, b, c.
Here,
* a means side opposite to A.
* b means side opposite to B.
* c means side opposite to C.
Triangle ABC

Now there is a term 'half perimeter' which is denoted by " s " in this formula.

Formula:

And finally the formula is given as:

Heron

Special Features:

* You do need to calculate height of triangle using complex geometric calculations.
* You just have to put the given sides in the formula and get the answer.

Related Resources:

Read related articles: Maths Formulas Mensuration Mathematics

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Responses to "Heron's formula."

Author: SAMYAK JAIN 21 Apr 2011

Member Level: Bronze Points : 1

If in a triangle all the three sides are given and we have to find the area of the given triangle then
First we have to find the semi-perimeter[s] of the triangle
s=sum of all the three sides divided by 2 or 1/2(a+b+c)
after getting 's' we have to find the area and the formula is
[vs(s-a)(s-b)(s-c)] or we can say that UNDER ROOT s(s-a)(s-b)(s-c)
WHERE A,B&C ARE THE SIDES OF THE TRIANGLE
LETS TAKE AN EXAMPLE
let the sides of an triangle be 40m,24m&32m and we have to find the area
so first we will find the semi-perimeter of the triangle by using the formula 1/2(a+b+c) so s=48m
now after getting 's' we will find the area by using the formula . and the formula is A=[vs(s-a)(s-b)(s-c)] so
(s-a)=(48-40)=8m
(s-b)=(48-24)=24m
(s-c)=(48-32)=16m
therefore the area will be
A=[vs(s-a)(s-b)(s-c)]=[v48(8)(24)(16)]m²=(v147456)m²=384m²

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