1. Heron’s Formula Winnie Liang Jessica Szela Emma Grace Medalla
Jenice Xiao
Algebra 2/Trigonometry Period 8

2. 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

3. 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.

4. A, B, and C are the sides of the triangle.
“S” is half the triangle’s perimeter

5. 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.

6. Examples:
What is the area of the triangle with sides of length 10 feet, 15 feet, and 17 feet?
S = 𝟏 𝟐 ( ) = 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

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

8. Now Try the Do Now Question
2) semiperimeter = a + b + c 2
s =
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)