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    Question

    In a cyclic quadrilateral, the diagonals intersect at an

    angle of 60°. If the sides of the quadrilateral are 6 cm, 8 cm, 10 cm, and 12 cm, what is the area of the quadrilateral? 
    A 48 cm² Correct Answer Incorrect Answer
    B 60 cm² Correct Answer Incorrect Answer
    C 76 cm² Correct Answer Incorrect Answer
    D 84 cm² Correct Answer Incorrect Answer

    Solution

    The area of a cyclic quadrilateral can be calculated using formula:  Area = √[(s - a)(s - b)(s - c)(s - d)],  where s = (a + b + c + d) / 2.  Here, s = (6 + 8 + 10 + 12) / 2 = 18 cm.  Area = √[(18 - 6)(18 - 8)(18 - 10)(18 - 12)] = √[12 × 10 × 8 × 6]  = √5760 = 75.89 cm² ≈ 76 cm². Correct answer: c) 76 cm²

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