Heron’s Formula Winnie Liang Jessica Szela Emma Grace Medalla

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Presentation transcript:

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. 6 in 8 in 1) 3 in 6 in 8 in 2) 1) Area of triangle = b h 2 A = 8  6 A = 48 A = 24 in2

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, Metrica written in 60 A.D. It was discovered by the Chinese published in Shushu Jiuzhang.

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 = 𝟏 𝟐 (10 + 15 + 17) = 21 area = 𝒔(𝒔−𝒂)(𝒔−𝒃)(𝒔−𝒄 ) area = 𝟐𝟏(𝟐𝟏−𝟏𝟎)(𝟐𝟏−𝟏𝟓)(𝟐𝟏−𝟕) area = 𝟐𝟏 𝟏𝟏 𝟔 𝟒 = 𝟓,𝟓𝟒𝟒 ≈𝟕𝟒.𝟒𝟓𝟖 square ft

2) What is the area of an equilateral triangle with all sides 6 inches in length? area = 𝟗(𝟑)(𝟑)(𝟑) = 𝟗 𝟏𝟑 ≈15.588 square in.

Now Try the Do Now Question 2) semiperimeter = a + b + c 2 s = 3 + 6 + 8 s = 17 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 3 in 6 in 8 in 2)