HERON’S FORMULA

W I N N I E L I A N G

J E S S I C A S Z E L A

E M M A G R A C E M E D A L L A

J E N I C E X I A O

A L G E B R A 2 / T R I G O N O M E T R Y P E R I O D 8

AIM: WHAT IS HERON’S FORMULA AND HOW DO WE USE IT?Do Now: Find the area.

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8 in

1)1) Area of triangle = b h 2

A = 8 6 2

A = 48 2

A = 24 in2

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8 in

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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.

“S” is half the triangle’s perimeter

A, B, and C are the sides of the

triangle.

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?

S = (10 + 15 + 17) = 21area = area = area = = square ft

2) What is the area of an equilateral triangle with all sides 6 inches in length?

s = (6 + 6 + 6) = 9area = 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

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8 in

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