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      Question

      A triangle ABC is inscribed in a circle with radius 10

      cm. The sides of the triangle are AB = 12 cm, BC = 16 cm, and AC = 20 cm. Find the area of the triangle.
      A Area = 96 cm² Correct Answer Incorrect Answer
      B Area = 99 cm² Correct Answer Incorrect Answer
      C Area = 100 cm² Correct Answer Incorrect Answer
      D Area = 100 cm² Correct Answer Incorrect Answer

      Solution

      Area of the triangle using Heron’s formula: Semi-perimeter, s = (AB + BC + AC) / 2 = (12 + 16 + 20) / 2 = 24 cm. Area = √[s(s - AB)(s - BC)(s - AC)] Area = √[24(24 - 12)(24 - 16)(24 - 20)] Area = √[24 × 12 × 8 × 4] Area = √9216 = 96 cm² Correct Option: a

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