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11.8: Hero’s and Brahmagupta’s Formula

11.8: Hero’s and Brahmagupta’s Formula. Hero’s Formula. A formula to find the area of any triangle if you know ALL three sides. a. b. a , b , c are sides of the triangle s = semi-perimeter (half the perimeter). c. Brahmagupta’s formula.

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11.8: Hero’s and Brahmagupta’s Formula

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  1. 11.8: Hero’s and Brahmagupta’s Formula

  2. Hero’s Formula • A formula to find the area of any triangle if you know ALL three sides. a b a,b,c are sides of the triangle s = semi-perimeter (half the perimeter) c

  3. Brahmagupta’s formula • A formula to find the area of any inscribed quadrilateral if you know ALL of the sides a b a,b,c,d are sides of the quadrilateral s = semi-perimeter (half the perimeter) d c

  4. Example 1 • Find the area. Express your answer as a simplified radical where appropriate. 12 12 10

  5. Example 2 • Find the area. Express your answer as a simplified radical where appropriate. 25 7 24

  6. Example 3 • Find the area. Express your answer as a simplified radical where appropriate. 31 7 5 35

  7. Example 4 • Find the area. Express your answer as a simplified radical where appropriate. 6

  8. Example 5 • Find the area. Express your answer as a simplified radical where appropriate. 7 5 9

  9. Example 6 • Find the area. Express your answer as a simplified radical where appropriate. 9 2 11

  10. Example 7 • Find the area. Express your answer as a simplified radical where appropriate. 4 3 10

  11. Homework p. 551 1, 3, 5-7, 9

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