Example 1 · level 1
A triangle has sides 5 cm, 5 cm and 8 cm. Find its area using Heron's formula (in cm²).
Show solution
- s = 18 ÷ 2 = 9.
- Area = √(9 × 4 × 4 × 1) = √144.
- = 12.
Answer: 12
CLASS 9 MATHS · HERON'S FORMULA
Heron's formula
With sides a, b, c and semi-perimeter s = (a + b + c)/2, area = √[s(s − a)(s − b)(s − c)].
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Worked examples
Example 2 · level 2
A triangle has sides 13 cm, 15 cm and 14 cm. Find its area using Heron's formula (in cm²).
Show solution
- s = 42 ÷ 2 = 21.
- Area = √(21 × 8 × 6 × 7) = √7,056.
- = 84.
Answer: 84
Example 3 · level 3
A triangular plot of land in Patna has sides 13 m, 20 m and 21 m. Find its area using Heron's formula (in m²).
Show solution
- s = 54 ÷ 2 = 27.
- Area = √(27 × 14 × 7 × 6) = √15,876.
- = 126.
Answer: 126