Heron was a Greek mathematician who lived around 0 AD and made significant contributions to mathematics. One of his most important contributions was Heron's formula, which allows users to calculate the area of a triangle when the lengths of all three sides are known. The formula calculates area as the square root of s(s-a)(s-b)(s-c), where s is equal to (a+b+c)/2 and a, b, and c are the lengths of the three sides of the triangle. The document provides an example of using Heron's formula to calculate the area of a triangle with side lengths of 3 cm, 5 cm, and 6 cm.

1. HERON’S FORMULA

2. HERON
Heron also known as Hero.
A Greek Mathematician.
When Heron lived is not
well established. Most
accounts place his life
around 0AD.
Heron’s formula is one of
his significant contribution.
Baroulkos, Geometrica,
Mechanica are Heron’s
famous books.

3. ABOUT HERON’S FORMULA
This gives the area of a triangle
when we know all three sides.
A way to calculate the area of any
quadrilateral.
A way to calculate the area of a
cyclic quadrilateral.

4. HERON’S FORMULA
a b
c
If a, b, c are three sides of a given triangle, then
according to Heron’s formula,
Area of the triangle = √s(s-a)(s-b)(s-c) , where
S= (a+b+c)/2.

5. AN EXAMPLE
Find the area of the following triangle?
3 cm 6 cm
5 cm

6. ANSWER
a= 3 cm , b= 5 cm , c= 6 cm
s= (a+b+c)/2
=(3+5+6)/2= 7 cm
Area of the triangle= √s(s-a)(s-b)(s-c)
=√7*(7-3)*(7-5)*(7-6)
=√7*4*2*1
=√56 square cm
=2√14 square cm

7. THE END