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    Question

    The sides of a triangle are 9 cm, 12 cm, and 15 cm. What is the area of the largest circle that can be inscribed in this triangle? 

    A 10 cm² Correct Answer Incorrect Answer
    B 15.42 cm² Correct Answer Incorrect Answer
    C 20 cm² Correct Answer Incorrect Answer
    D 28.26 cm² Correct Answer Incorrect Answer

    Solution

    The triangle is a right triangle. The area A = (1/2) × base × height = (1/2) × 9 × 12 = 54 cm². The semiperimeter s = (9 + 12 + 15) / 2 = 18 cm. The inradius r = A / s = 54 / 18 = 3 cm. The area of the inscribed circle is πr² = π(3)² = 9π ≈ 28.26 cm². Correct answer: d) 28.26 cm²

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