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Aim: How can we find the area of a Triangle using Heron’s Formula

Aim: How can we find the area of a Triangle using Heron’s Formula. Do Now:. A. Find the area of triangle ADC. Round to the nearest tenth. 12. X. Answer: Area=35.8. C. 8. B. Facts About Heron’s Formula.

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Aim: How can we find the area of a Triangle using Heron’s Formula

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  1. Aim: How can we find the area of a Triangle using Heron’s Formula Do Now: A Find the area of triangle ADC. Round to the nearest tenth. 12 X Answer: Area=35.8 C 8 B

  2. Facts About Heron’s Formula • The formula is credited to Heron of Alexandria, who was an ancient Greek mathematician and engineer who was active in his native city of Alexandria, Roman Egypt. • Hero also described a method of iteratively computing the root. Today however, his name is most closely associated with Heron’s Formula for finding the area of a triangle from its side lengths and a proof can be found in his book, Metrica, which was written c. A.D. 60. • It has been suggested that Archimedes knew the formula, and since Metrica is a collection of the mathematical knowledge available in the ancient world, it is possible that it predates the reference given in the work. • A formula equivalent to Heron's namely: • , where  • was discovered by the Chinese independently of the Greeks.

  3. HERON’S FORMULA: • Heron’s Formula is used to get the area of a triangle when you know the sides of the triangle, but you do not know the height. • Step 1: Find the semi-perimeter – half the perimeter of the triangle. • Step 2: Plug “s” into the formula and solve. • Heron’s Formula is also used as an equivalent to the Pythagorean theorem. A C B

  4. Example 1: What is the area of a triangle where every side is 5 long? 5 5 5 Answer- Step 1: S = (5+5+5)/2 = 7.5 Step 2: A = √(7.5 × 2.5 × 2.5 × 2.5) = √(117.1875) = 10.825...

  5. Example 2: • Use Heron’s Formula to find the area. Round to the nearest tenth. 3 7 6 Answer- Step 1: 7+3+6/2=8 Step 2:√8(8-7)(8-6)(8-3)=√(80)=8.9

  6. Example 3: • Find the Area using Heron’s Formula. 30 Answers Step 1:27.5 Step 2: 141.989 18 24

  7. Proof With Heron’s Formula: Area Law of Cosines

  8. Proof With Heron’s Formula: Pythagorean Theorem

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