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      Question

      The sides of a triangle are 10 cm, 17 cm, and 21 cm.

      Find the area of the triangle using Heron’s formula.
      A 80 cm² Correct Answer Incorrect Answer
      B 84 cm² Correct Answer Incorrect Answer
      C 96 cm² Correct Answer Incorrect Answer
      D 102 cm² Correct Answer Incorrect Answer

      Solution

      Let the sides of the triangle be a = 10 cm, b = 17 cm, c = 21 cm. The semi-perimeter (s) is: s = (a + b + c)/2 = (10 + 17 + 21)/2 = 24 cm. The area of the triangle is given by: Area = √[s(s - a)(s - b)(s - c)] = √[24(24 - 10)(24 - 17)(24 - 21)] = √[24 × 14 × 7 × 3] = √[24 × 294] = √7056 = 84 cm². Correct answer: b. 84 cm²

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