The document presents information about Heron's formula for calculating the area of a triangle when the lengths of all three sides are known. It defines Heron's formula as the square root of s(s-a)(s-b)(s-c)/2, where s is the semi-perimeter or half the perimeter, and a, b, c are the lengths of the three sides. It also provides some biographical details about Heron, the Greek mathematician who developed the formula, and demonstrates solving an example using the formula.

1. PRESENTATION
ON
HERON’S FORMULA
Made by:- Kapil Jain
Class:-9th

2. INTRODUCTION
*Area:- Area is the size of a surface.
*In earlier classes, we have studied, how to find
an area and perimeter of a triangle.
*Perimeter :- Perimeter is the sum of all sides.

3. AREA AND PERIMETER OF
A TRIANGLE
Area of triangle-1/2 × base × height
Perimeter-sum of all sides of triangle
Perimeter= sum of all sides
=5+5+8
=18cm
Area=1/2 ×base ×height
=1/2 ×8 ×6
=1/2×48
=24m2
8cm
6cm

4. Types of
triangles
Equilateral
triangle
Isosceles
triangle
Right angle
triangle
Scalene
triangle

5. HERON’SFORMULA
*Definition:- Heron’s formula is used to find the area of
triangle when the length of all sides is known.
*Area of triangle=√
───────────
*In this formula a , b ,and c are the sides of the triangle ,and s
represent semi perimeter is half of perimeter of the triangle
= a+b+c
─────
*This formula is given by Heron’s.
s(s-a)(s-b)(s-c)
2

6. SOME INFORMATION ABOUT
HERON
*Heron was born in 10AD in Egypt and his
full name is Heron ho Alexandria.
*He also know as Hero of Alexandria.
*He was a Greek mathematician and
engineer.
*He also know for Heron’s fountain,
Heron’s formula, and Vending machine.

7. IMPORTANCE OF HERON’S FORMULA
This formula is helpful where it is not
possible to find height of the triangle
easily.
It is also helpful in finding area of
triangle.

8. Q- Find the area of triangle whose sides are 3cm,
4cm and 5cm respectively?
Solution:
───────
Area of triangle = √
──────────
= √
──────────
= √
──────────
= √36
= 6cm2
2
2
s(s-a)(s-b)(s-c)
6(6-3)(6-4)(6-5)
6×3×2×1
a= 3cm
b= 4cm
c= 5cm
S[semi perimeter]= a+b+c
───────
=3+4+5