It is an perfect ppt for class 9 student to learn or to score marks. It has good question on herons theorm.You will comfortable after download.

3. S.No Title Page.No
01. Introduction 04
02. Acknowledgement 05
03. Content 06
04. Theory 07-18
05. Conclusion ,Bibliography ,Thanks Page 19,21

4. GROUP=6
Name=Kumar Ayush, Samear Kumar, Pravesh, Prabudh
Gaurav, Shivam Singh,Shudhanshu Ranjan.
Class=9th / B.
Subject= Math's.
School= Erny Memorial Senior Secondary School .

5. First we give thanks to our special math's teacher
(Deepika Borrison) for giving us such a great
project on Herons Formula.
We learn that to calculate the area of a triangle if
you know the lengths of all three sides, using a
formula that has been known for nearly 2000
years.
It is called "Heron's Formula" after Hero of
Alexandria .And the beautiful history of Herons .
We also know that the everyday use of herons
formula. We also know about the books written
by sir Heron.

6. CONTENTS
Heron’s Formula
About Heron Needs of Heron’s
Formula
Area of Triangles
and some other
shapes
Questions

7. In geometry, Heron's formula(sometimes called Hero's formula), named after Hero of Alexandria,[1]gives
the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other
formulas for the area of a triangle, such as half the base times the height or half the norm of a cross product of
two sides.
Heron’s Formula
Let there be a scalene triangle, the lengths of its sides are known but the height is not known. To find its area
none of above listed formulae is applicable. In fact, we require the height corresponding to a base. But we do
not have any clue for the same.
We have to use Herons Formula their.

8. About Heron
Heron, (also known as Hero) was a Greek mathematician. Some
authorities place his birthday early 150 BCE in Ptolemaic, Egypt. While
other scholars have dated his birth to be 250 CE in late Roman Empire.
Nothing is really known of Hero's life, but what we do know comes from
clues in the 14 known books by him.
He was an accomplished inventor and mechanical engineer. Among his
inventions were a
reaction steam turbine, a
vending machine, and a
wind-powered organ.

9. Some of Heron's books
Baroulkos
Berlopoeica (in Greek and Roman Artillery, Technical Treatises, 1971)
Catoptrica (in Latin)
Chieroballistra (in Greek and Roman Artillery; Technical Treatises, 1971)
Dioptra (partical English translation, 1963)
Eutocuis
Geometrica
Mechanica (3 volumes, in Arabic)
Metrica (3 volumes)
Peri Automatopoitikes (Automata, 1971)
Peri Metron (also called Mensurae)
Pneumatica (2 volumes: The Pneumatica of Hero Of Alexandria, 1851)
Stereometrica

10. We can calculate the area of a triangle if we know the lengths
of all three sides, using a formula that has been known for
nearly 2000 years.
It is called "Heron's Formula" after Hero of Alexandria
The formula can be written as :
S=

11. Need of Heron's Formula
Herons formula can be used to measure the area of a triangle whose sides are given. It helps you to find the area
of a triangle where the height is not given. This includes scalene, isosceles and equilateral triangles
It can be used in our daily life in the following ways.-
(i) When we buy a piece of land we can find its area by using herons formula
(ii) Imagine someone gave you a triangular figure(it can be 2d or 3d) now u can find its area by just applying
herons formula.

12. Formulas of some shapes which are
related to Heron’s Formula.
Rectangle Square
If a denote the length of each side of a
square , then
(i) Perimeter = 4a
(ii) Area = a² = (side)²
(iii) Area = ½ (Diagonal)²
If l and b denote respectively the length
and breadth of a rectangle, then
(i) Perimeter = 2(l + b)
(ii) Area = l x b

13. ParallelogramRhombus
i) Perimeter = 2(AB +
BC) = 2(l + b )
(ii) Area = Base x
Height
If d1 and d2 are the lengths
of the diagonals of a
rhombus of side a, then
(i) Perimeter = 4a = 4(side)
(ii) Area = ½ (d1 x d2)

14. 1.Find the area of a quadrilateral ABCD in
which AB = 3 cm, B = 90°CD = 4 cm, DA = 5
cm, and AC = 5 cm.
5cm
4cm
3 cm
D
A B
C
Solution
Area of ∆ ABC = ½ × AB × BC
= ( ½ × 3 × 4) cm²
= 6 cm²
For Δ ACD:
Let a = 5 cm, b = 4 cm
and c = 5 cm. then,
s = ½ × (a + b + c)
s = ½ ( 5 + 4 + 5 )
cm
s = ½ × 14 cm
s = 7 cm
FIGURE

15. Now, s – a = ( 7 – 5 ) = 2 cm
s – b = ( 7 – 4 ) = 3 cm
s – c = ( 7 – 5 ) = 2 cm
Area of ∆ ACD = √s(s — a)(s —
b)(s—c)
= √ 7 (2) (3) (2)
= √ 2 × 2 × 3 × 7
= 2 × √3 ×√7
= 2 × √21
= 2 × 4.58 =
9.167 /
-
Area of quadrilateral ABCD =
Area of ∆ABC + Area of ∆ ACD
= 6 + (9.16) cm²
= 15.2 cm² (approx.)

16. (2) The sides of a triangle are 11 cm, 13 cm and 20 cm. The altitude to the longest
side is :
Solution
Step 1
Let's assume the altitude to the longest side be 'h'.
Following picture shows the required triangle,
The area of the triangle ΔABC can be calculated using Heron's formula, since
all sides of
the triangles are known.
S = (AB + BC + CA)/2
= (20 + 13 + 11)/2
= 22 cm.
The area of the ΔABC = √[ S (S - AB) (S - BC) (S - CA) ]
= √[ 22(22 - 20) (22 - 13) (22 - 11) ]
= 66 cm2

17. Step 2
The altitude to the longest side =
2 × (The area of the ΔABC)
Base 'AB'
=
2 × 66
20
= 6.6 cm.
3. The triangle wall of a flyover have
been used for advertisement. The sides
of the walls are 122m, 22m, and 120m
(see the given figure). The
advertisements yield
an earning of Rs 5000 per m2 per year.
A company hired one of its walls for 3
months. How much rent did it pay?
FIGURE

18. Solution

19. Conclusion
We learn that to calculate the area of a triangle if you know
the lengths of all three sides, using a formula that has been
known for nearly 2000 years.
It is called "Heron's Formula" after Hero of Alexandria .And the
beautiful history of Herons . We also know that the everyday
use of herons formula. We know the books written by sir
Heron.

20. BIBLIOGRAPHY
In this PowerPoint Presentation we have take help of
internet. The site is www.google.com
,www.wikipidia.com
.
We also take help of Math’s NCERT text book and R.D
Sharma. For some information help. With these help
our team (group-6) had made this help.