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11.8 Hero’s and Brahmagupta’s Formulas Objective: After studying this section you will be able to find the areas of figures by using Hero’s and Brahmagupta’s.

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Presentation on theme: "11.8 Hero’s and Brahmagupta’s Formulas Objective: After studying this section you will be able to find the areas of figures by using Hero’s and Brahmagupta’s."— Presentation transcript:

1 11.8 Hero’s and Brahmagupta’s Formulas Objective: After studying this section you will be able to find the areas of figures by using Hero’s and Brahmagupta’s formula

2 Theorem Where a, b, and c are the lengths of the sides of the triangle, and s = semiperimeter =. A long time ago (about 2000 years) a mathematician known as Hero of Alexandria developed a formula for finding the area of a triangle. It is as follows: b a c

3 Theorem Where a, b, c, and d are the sides of the quadrilateral and s = semiperimeter =. In about 628 A.D., a Hindu mathematician named Brahmagupta found a formula for the area of an inscribed quadrilateral. Warning: This only applies to quadrilaterals that can be inscribed in circles AKA Cyclic Quadrilaterals! b a c d

4 Example #1: Find the area of a triangle with sides 3, 6, and 7. Answer:

5 Example #2: Find the area of the inscribed quadrilateral with sides 2, 7, 6, and 9 Answer: 30 9 7 6 2

6 Homework: Worksheet 11.8

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