Herons Formula

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Herons Formula

  1. 1. Heron’s formula
  2. 2. Introduction to heron’s formula
  3. 3. Introduction of another formula for area of a triangle • Most of us are aware with : • Area of a triangle = Where b = base and h = corresponding height of the triangle
  4. 4. Examples : • 1) Find the area of a triangle having sides : AB = 4 cm BC = 3 cm CD = 5 cm
  5. 5. Solution of Example 1)
  6. 6. Continue…
  7. 7. Example 2: 2) Rahul has a garden, which is triangular in shape. The sides of the garden are 13 m, 14 m, and 15 m respectively. He wants to spread fertilizer in the garden and the total cost required for doing it is Rs 10 per m2 . He is wondering how much money will be required to spread the fertilizer in the garden
  8. 8. Solution of Example 2) • Given a = 13 m , b = 14 m and c = 15 m So , we will find the area of the triangle by using Heron’s formula.
  9. 9. Continue.. 21(21 13)(21 14)(21 15)− − − 21*8*7 *6=
  10. 10. Continue … • Given the rate = Rs 10 per m^2 • Now : • Total cost = Rs. 10 * 84 = Rs 840/-
  11. 11. Area of a quadrilateral • Suppose there is a quadrilateral having sides : a , b , c and d and diagonal r. The diagonal d divides the quadrilateral into 2 triangles. So : Ar(ABCD)= Ar(ABD) + Ar(BCD)
  12. 12. Continued 1) Area of triangle : ABD Heron’s formula: Putting the values we get :
  13. 13. Continued..
  14. 14. Solution of example As we have the formula written below for the area of a quadrilateral Where : a = 4cm b = 3 cm c = 5 cm d = 6 cm And r (diagonal ) = 7 cm
  15. 15. cm2 Click on this arrow to continue
  16. 16. How to find the area of an equilateral triangle
  17. 17. Concept based question • What equilateral triangle would have the same area as a triangle with sides 6, 8 and 10?
  18. 18. Solution • First of all we will find the area of the triangle having sides : a = 6 units , b = 8 units and c = 10 units

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