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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 HeronтАЩs formula.
    A 80 cm┬▓ Correct Answer Incorrect Answer
    B 84 cm┬▓ Correct Answer Incorrect Answer
    C 96 cm┬▓ Correct Answer Incorrect Answer
    D 102 cm┬▓ 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 = тИЪ[s(s - a)(s - b)(s - c)] = тИЪ[24(24 - 10)(24 - 17)(24 - 21)] = тИЪ[24 ├Ч 14 ├Ч 7 ├Ч 3] = тИЪ[24 ├Ч 294] = тИЪ7056 = 84 cm┬▓. Correct answer: b. 84 cm┬▓

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