Heron’s formula

ppt on heron's formula based on class 9 course

1. HERON’S FORMULA CHAPTER - 12

2. INTRODUCTION In earlier classes we have study to find an area and perimeter of a triangle You know perimeter is sum of all sides of the given triangle And also area is equal to the total potion covered in a triangle

3. Area and perimeter of a triangle Till now we are knowing that – Area of triangle = ½ * base * height 5 cm 5 cm 8 cm Here in given triangle – Perimeter = sum of all sides = 5+5+8 = 18 cm Area = ½ * base * height Area = ½ * 8 * 6 Area = 24 cm 6 cm 2

4. TYPES OF TRIANGLES

5. 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. 12 cm 8 cm 5 cm Consider the following figure – Base = 5 cm Height = 8 cm Area = ½ * 8 * 5 = 20 cm 2

6. AREA OF EQUILATERAL TRIANGLE Now we will try to find the area of an equilateral triangle with side 10 cm 5 cm 10 cm 10 cm Here, we can find height by pythagoras theorem So here height = √ 75 = 5√3 Area = ½ * base * height = ½ * 10 * 5√3 = 25 √3 cm 2

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

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.

11. GROUP MEMBERS KINSHUK NEEMA SHUBHANSHU MUKATI ANUJ GUPTA AKASH GIRI