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    Question

    In a triangle ABC, the sides are AB = 15 cm, BC = 20 cm,

    and AC = 25 cm. Find the area of the triangle using Heron’s formula.
    A 150 cm² Correct Answer Incorrect Answer
    B 120 cm² Correct Answer Incorrect Answer
    C 100 cm² Correct Answer Incorrect Answer
    D 180 cm² Correct Answer Incorrect Answer

    Solution

    The semi-perimeter of the triangle is given by: s = (AB + BC + AC) / 2 s = (15 + 20 + 25) / 2 = 30 cm Now, using Heron’s formula: Area = √[s(s − AB)(s − BC)(s − AC)] Area = √[30(30 − 15)(30 − 20)(30 − 25)] Area = √[30 × 15 × 10 × 5] Area = √22500 Area = 150 cm² Correct answer: a) 150 cm²

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