I can say this power point will help you to know about "HERON’S FORMULA". You will understand the meaning of 'HERON’S FORMULA'.This power point is best for class 9. Monish Jeswani. Thank You!!!!

1. HERON’S FORMULA
BY-
Monish
Jeswani

2. INTRODUCTION
• We know the formula to find area of different
plane figures like - Square, Rectangle, Right-
angled Triangle, Isosceles Triangle, Equilateral
Triangle, parallelogram Rhombus etc .
• But, in a scalene triangle, Finding its area is
difficult. All the known formula uses triangle’s
height to find the area of triangle.
• Heron(10AD – 75 AD), mathematician from Egypt
derived a formula for finding area of triangle in
terms of lengths of its 3 sides .

3. Derivation
Consider a scalene triangle as shown in the
following figure. a, b, c are the Length of
three sides, which are known. Height h, length
d and length c-d are unknown.
Semi-perimeter s of Triangle = (a+b+c) / 2

4. By the Pythagorean theorem we have
and
Subtract (1) from (2)
- - - - - - - - - - - - (1)
- - - - - - - - - - - - (2)
a² - b² = h²+(c-d)²- [h²+d²]
= h²+(c-d)²- h²-d²
= c²-2cd+d²-d²
= c² - 2cd

5. Thus,
Here d is unknown, Therefore express d in terms
Of known lengths, we have –
2cd = - a²+b² +c²
or
Again From Figure, using Pythagorean theorem
- - - - - - - - - - - - - - - - (3)
- - - - - - - - - - - - - - - - - - (5)
- - - - - - - (4)

6. • Put value of d from equation (4) in
equation (5). Thus,
- - - - - - - - - - - (6)

7. Area of Triangle = ½ Base x height
= ½ c x h
Put value of h from equation (6), we get area of
triangle A as :

8. Importance
• Makes it easy to calculate area of any triangle
whose lengths are known. Thus, it is very
convenient to find or measure the area of
field.

9. Application
• Heron’s formula is applicable to find the area
of all types of triangles.

10. Conclusion
• So this is the simplest way of finding area of
triangle with all sides known.

11. Thank you !