Quick answer: Heron's formula gives triangle area Δ = √[s(s − a)(s − b)(s − c)], where s = (a + b + c)/2. It is useful when all three sides are known and no height is given.
Worked example
Find the area of a triangle with sides 13 cm, 14 cm and 15 cm.
- s = (13 + 14 + 15)/2 = 21 cm.
- s − a = 8, s − b = 7, s − c = 6.
- Area = √(21 × 8 × 7 × 6) = √7056.
- Area = 84 cm².
Check the result
Using base 14 cm, the implied altitude is 2×84/14 = 12 cm; √(13² − 12²) + √(15² − 12²) = 5 + 9 = 14.
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Common mistake to avoid
Use semiperimeter, not perimeter. Check triangle inequality first; impossible side lengths are not valid inputs.
Try it yourself
1. Find area of a 3, 4, 5 triangle. 2. Can sides 2, 3, 6 form a triangle?
Answers and reasoning
1. s = 6; area = √(6×3×2×1) = 6 square units. 2. No: 2 + 3 < 6.
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