Showing you some slides that explain the concepts of Heron's formula.

2. • Objectives:-
• Perimeter of Triangle
• Area of Triangle
• Area of Triangle by Heron’s
Formula
HERON’S FORMULA

3. INTRODUCTION:-
• In earlier classes we have studied to find
an area and perimeter of a triangle
• Perimeter is sum of all sides of the given
triangle
• Area is equal to the total portion covered
in a triangle

4. AREA AND PERIMETER OF AN
TRIANGLE:-
• Area of triangle = ½ x base x height
• Perimeter = sum of all sides of triangle
• Perimeter = sum of all sides
= 5 + 5 + 8
= 18 cm
• Area = ½ x base x height
• Area = ½ x 8 x 6
• Area = 24 sq. cm
5 cm
5cm
6cm
8cm

5. Equilateral Triangle
Isosceles Triangle
Scalene Triangle
Right Angle Triangle
TYPES OF
TRIANGLES:-

6. AREA OF EQUILATERAL TRIANGLE
• Find the area of an equilateral triangle with side 10 cm.
• Here, we can find height by pythagoras theorem .
• So here height = √75
= 5√3
• Area = ½ x base x height = ½ x 10 x 5√3
= 25√3 cm2
10 cm 10
cm
5 cm

7. AREA OF RIGHT ANGLE TRIANGLE
• In a right angle triangle we can directly apply the formula to find
the area of the triangle, as two sides containing the right angle as
base and height.
• Consider the following figure – Base = 5 cm
Height = 8 cm
• Area = ½ x 8 x 5
= 20 cm2
5 cm 12
cm
5cm

8. AREA OF ISOSCELES TRIANGLES
• Find out the area of an isosceles triangle whose 2 equal
sides are 5 cm and the unequal side is 8 cm 8 cm 4 cm .
• Here height can be find by pythagoras theorem So, h = 3 cm
• Area = ½ x base x height
= ½ x 8 x 3
= 12 cm2
5 cm
5 cm
4cm 8 cm

9. AREA OF
TRIANGLE BY
HERON’S FORMULA
Heron was born in about
10AD possibly in Alexandria
in Egypt. His works on
mathematical and physical
subjects are so numerous
and varied that he is
considered to be an
encyclopedic writer in these
fields. His geometrical
works deal largely with
problems on mensuration.
He has derived the famous
formula for the area of a
triangle in terms of its
three sides. HERON (10AD
- 75AD)

10. HERON’S FORMULA
• Area of triangle = √s(s-a)(s-b)(s-c)
• Where a , b and c are the sides of
the triangle , and s = semi perimeter,
i.e., half of perimeter of the triangle
= a + b + c /2

11. 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 quadrilaterals.
• Q- Find the area of triangle whose sides are 3cm, 4cm & 5
cm respectively.
• Area of triangle = √s(s-a)(s-b)(s-c)
= 3+4+5 = 6 2
• Area of triangle = √6(6-3)(6-4)(6-5)
= √ 6 x 3 x 2 x 1 = 6 cm²
• As s = a + b + c 2

12. SUBMITTED BY :- RAMANPREET
KAUR
CLASS :-9TH ‘A’
ROLL NO. :- 26
R.D . Khosla . D . A .V Model .
Sr . Sec School , Batala