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    Question

    A triangle has sides 7 cm, 24 cm, and 25 cm. A circle is

    inscribed in the triangle. What is the area of the triangle not covered by the circle?
    A 48 cm² Correct Answer Incorrect Answer
    B 55.74 cm² Correct Answer Incorrect Answer
    C 96 cm² Correct Answer Incorrect Answer
    D 68.55 cm² Correct Answer Incorrect Answer

    Solution

    The area of the triangle is A = (1/2) × base × height = (1/2) × 7 × 24 = 84 cm². The semiperimeter s = (7 + 24 + 25) / 2 = 28 cm. The inradius r = A / s = 84 / 28 = 3 cm. The area covered by the circle is πr² = π × 9 ≈ 28.26 cm². The remaining area = 84 - 28.26 = 55.74 cm². Correct answer: b) 55.74 cm²

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