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)
1)
2)
Area of triangle = b h
2
A =86
2
6 in
A = 48
2
8 in
A = 24 in2
3 in
6
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, 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:
1) What is the area of the triangle with sides of
length 10 feet, 15 feet, and 17 feet?
𝟏
𝟐
S = (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?
s=
𝟏
(6
𝟐
area =
area =
area =
+ 6 + 6) = 9
𝒔(𝒔 − 𝒂)(𝒔 − 𝒃)(𝒔 − 𝒄)
𝟗(𝟗 − 𝟔)(𝟗 − 𝟔)(𝟗 − 𝟔)
𝟗(𝟑)(𝟑)(𝟑)= 𝟗 𝟏𝟑 ≈15.588 square in.
NOW TRY THE DO NOW QUESTION
2)
3 in
6
in
8 in
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