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.

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.

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

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.