Calculate the area of a triangle given the lengths of all three sides (Heron's Formula).
Side Lengths
Triangle Analysis
10.8253u²
Total Area
Perimeter15.00
Semi-perimeter (s)7.50
Triangle TypeEquilateral
Hero of Alexandria's Formula
Heron's formula allows you to calculate the area of a triangle without knowing its height or any of its angles. It is named after Heron of Alexandria, a mathematician from the 1st century AD. It relies purely on the lengths of the three sides.
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Pro Tips
The sum of any two sides must be greater than the third side (Triangle Inequality Theorem).
If the sides don't form a valid triangle, the area will be mathematically undefined.
This formula is great for surveyors calculating land area from boundary measurements.
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Fun Facts
"Hero of Alexandria was also credited with inventing the first steam engine, the aeolipile."
"A triangle with sides 3, 4, 5 has an area of exactly 6 square units."
"The formula can be derived directly from the Law of Cosines."
Formula: Area = √[s(s - a)(s - b)(s - c)], where s = (a + b + c) / 2
