Heron's formula

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

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

2. 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

3. 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. c m 5 cm 5cm 6cm 8cm

4. TYPES OF TRIANGLES:-

5. 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

6. AREA OF RIGHT ANGLE TRIANGLE I n 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

7. AREA OF ISOSCELES TRIANGLES F ind 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

8. 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)

9. 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

10. 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

11. Submitted By :- Ramanpreet Kaur class :-9 th ‘a’ roll no. :- 26 R.D . Khosla . D . A .V Model . Sr . Sec School , Batala