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common core standard
Common Core Standard
6.G.1
​Why is this triangle area formula named “Heron’s formula?” The formula is named after Heron of Alexandria, but some historians argue that the formula was actually proposed by Archimedes who was an ancient Greek Mathematician, and a brilliant mind of his time. In addition, Qin Jiushao, a Chinese Mathematician, had a similar formula that he recorded in, “Mathematical Treatise in Nine Sections.”
Heron wrote many treaties, and at least 14 have been uncovered. The subjects covered included toys, machines, an organ, and even a fire engine. His treaty titled “ Metrica” was three books dealing with Geometry. It included formulas for finding the area, and volume of geometric shapes. Included in these three books was a formula for finding the area of a triangle if the altitude is missing, which eventually became, “Heron’s formula.” One reason that this formula is still taught today is that Mathematical truth is eternal, and it allows one to calculate the area of a triangle using just side measurements.

Heron's Formula history

Heron's Formula step by step

Questions answered in this video...

How do use Heron's formula to find the area of a triangle that has sides of 4,4, and 6 units?

What is the formula for "s"

Can you find the area of a triangle if height is not given?






check answer here
Questions answered in this video...

How do you find the area of a triangle with sides of 6,8, and 12 units with no height provided?

What is the formula for finding the area of a triangle?

How do use Heron's formula to find the area of a triangle?

How do you find "s" ?




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video tutorial heron's formula
heron's formula example problem

Heron's Formula-Area of a triangle



Example 1 Find the area of a triangle with lengths of 5, 6, and 7 units.
area of triangle
5
7
6
Example problem 2: Find the area of a triangle with sides of 6 units,8 units, and 12 units. No altitude is given.
finding the area of triangle
6
8
12
How to use Heron's formula to calculate the area of a triangle
Step 2. Plug s into the formula 
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Example problem 3: Find the area of a triangle with sides of 7 units,8 units, and 12 units. No altitude is given. Since, the altitude is missing you can use Heron's formula.
check answer here
8 by 12 by 7 triangle
Example problem 4: Find the area of a triangle with sides of 4 units,4 units, and 6 units. No altitude is given. Hint, use Heron's Formula
check answer
4 x4x6  triangle
Formula for triangle
Triangle no height
s Heron's formula
Heron's formula
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Triangle Area using Heron's Formula

Step 1. Find s using 
What formula for a triangle can is used if you know three sides of a triangle but you don't know the altitude? The area of a triangle can be calculated using Heron's formula.