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 the area of a triangle from its three side lengths alone, without needing the height. It was discovered by the ancient Greek mathematician Hero of Alexandria.
- 1s = (a + b + c) / 2 (semi-perimeter)
- 2Area = √(s(s−a)(s−b)(s−c))
- 3Works for any triangle given three sides
- 4Triangle inequality must hold: each side < sum of other two
Sides 3, 4, 5=s=6, Area = √(6×3×2×1) = 6
Sides 5, 5, 6=s=8, Area = √(8×3×3×2) = 12
| a | b | c | Area |
|---|---|---|---|
| 3 | 4 | 5 | 6 |
| 5 | 5 | 6 | 12 |
| 6 | 8 | 10 | 24 |
| 7 | 8 | 9 | 26.83 |
References
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