Question
Find the area of a triangle with sides 13 cm, 14 cm and
15 cm.Solution
Use Heron’s formula. Semi‑perimeter s = (13 + 14 + 15)/2 = 42/2 = 21 Area = √[s(s − a)(s − b)(s − c)] = √[21(21 − 13)(21 − 14)(21 − 15)] = √[21 × 8 × 7 × 6] Compute inside: 21 × 8 = 168 7 × 6 = 42 168 × 42 = (168 × 40) + (168 × 2) = 6,720 + 336 = 7,056 Area = √7,056 But notice: 7,056 = 84² (since 80²=6,400; 84²=7,056) So Area = 84 cm² Answer: 84 cm².
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