# Heron’s formula explained with example

Learn and know the Heron’s formula which is very useful in finding area of a triangle when its sides are given. This is the one of the important formula related to triangle. In CBSE class 9 mathematics book we can observe one total chapter is on Heron’s formula. Those who have completed 9th class they may be know this formula.

Do you know who introduced Heron’s formula? A mathematician called Heron who was born in Alexandria which is located in Egypt has introduced it. When only sides are known for any given triangle, then by using Heron’s formula we can find its area.

## The Heron’s formula as follows:

The Heron’s formula used for finding the area of a triangle is given by

In the formula a, b, and c are sides of the triangle and “s” is called as semi perimeter. Semi perimeter is sum of all the sides (a + b + c) divided by 2.

Semi perimeter formula:

Semi perimeter, S = $\frac { \left( a+b+c \right) }{ 2 }$

Example:

Can you find what is the area of a triangle whose sides are given as 15 cm, 5 cm and 20 cm?

Solution:

Given sides are a = 15 cm, b = 8 cm and c = 20 cm.

Note:

Do you know how to represent sides of a triangle? Remember that we should always represent sides of a triangle as given below

Opposite to vertex A we should represent “a” cm

Opposite to vertex B we should represent “b” cm

Opposite to vertex C we should represent “c” cm

Sum of the sides = 15 + 9 + 20

= 44 cm

Therefore semi perimeter, S = $\frac { 44 }{ 2 }$ = 22

We know the area of a triangle formula,

= 65.67 ${ cm }^{ 2 }$

Hope that you have understood Heron’s formula and its application i.e. how to find the area of triangle.

I will give you one problem, you just find out the area by using the formula.

Find the area of triangle whose sides are given as 12cm, 10cm and 4cm. let me know what answers you got?