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Heron’s Formula. Winnie Liang Jessica Szela Emma Grace Medalla Jenice Xiao Algebra 2/Trigonometry Period 8. Aim : What is Heron’s Formula and how do we use it?. Do Now : Find the area. 1). 2). 1) Area of triangle = b h 2
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Heron’s Formula Winnie Liang Jessica Szela Emma Grace Medalla Jenice Xiao Algebra 2/Trigonometry Period 8
Aim:What is Heron’s Formula and how do we use it? Do Now: Find the area. 1) 2) 1) Area of triangle = bh 2 A = 8 6 2 A = 48 2 A = 24 in2 3 in 6 in 6 in 8 in 8 in
The Heron’s formula is used to find the area of a triangle using its sides. The formula is credited to Heron, who was the “Hero of Alexandria”; a proof can be found in his book, Metricawritten in 60 A.D. It was discovered by the Chinese published in ShushuJiuzhang.
A, B, and C are the sides of the triangle. • “S” is half the triangle’s perimeter
The Heron’s formula: After using the formula to find “s,” you plug it into the Heron’s formula and again a, b, and c refer to the sides of the triangle.
Examples: • What is the area of the triangle with sides of length 10 feet, 15 feet, and 17 feet? S = (10 + 15 + 17) = 21 area = area = area = = square ft
2) What is the area of an equilateral triangle with all sides 6 inches in length? s = (6 + 6 + 6) = 9 area = area = area = = 15.588 square in.
Now Try the Do Now Question 2) semiperimeter = a + b + c 2 s = 3 + 6 + 8 2 s = 17 2 s = 8.5 A = √s(s – a)(s – b)(s– c) A = √8.5(8.5 – 3)(8.5 – 6)(8.5 – 8) A = √8.5(5.5)(2.5)(0.5) A ≈ 7.64 in2 2) 3 in 6 in 8 in
