Question
Find the area of a triangle with sides 13 cm, 14 cm and
15 cm.Solution
Use Heronâs formula. Semiâperimeter s = (13 + 14 + 15)/2 = 42/2 = 21 Area = â[s(s â a)(s â b)(s â c)] = â[21(21 â 13)(21 â 14)(21 â 15)] = â[21 Ă 8 Ă 7 Ă 6] Compute inside: 21 Ă 8 = 168 7 Ă 6 = 42 168 Ă 42 = (168 Ă 40) + (168 Ă 2) = 6,720 + 336 = 7,056 Area = â7,056 But notice: 7,056 = 84² (since 80²=6,400; 84²=7,056) So Area = 84 cm² Answer: 84 cm².
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