Heron's Formula — Triangle Area
Side a
Side b
Side c
Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2
Heron's formula calculates triangle area from three side lengths. Named after Hero of Alexandria (c. 10–70 AD), it requires no height measurement.
- 1Compute s = (a+b+c)/2
- 2Area = √(s·(s−a)·(s−b)·(s−c))
- 3Verify triangle inequality first
- 4Result is exact for integer sides
a=3, b=4, c=5=Area = 6 (right triangle)
a=13, b=14, c=15=Area = 84
| Sides | Area |
|---|---|
| 3,4,5 | 6 |
| 5,12,13 | 30 |
| 8,15,17 | 60 |
| 13,14,15 | 84 |
References
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