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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?┬а
    A 48 cm┬▓ Correct Answer Incorrect Answer
    B 60 cm┬▓ Correct Answer Incorrect Answer
    C 76 cm┬▓ Correct Answer Incorrect Answer
    D 84 cm┬▓ Correct Answer Incorrect Answer

    Solution

    The area of a cyclic quadrilateral can be calculated using formula:┬а Area = тИЪ[(s - a)(s - b)(s - c)(s - d)],┬а where s = (a + b + c + d) / 2.┬а Here, s = (6 + 8 + 10 + 12) / 2 = 18 cm.┬а Area = тИЪ[(18 - 6)(18 - 8)(18 - 10)(18 - 12)] = тИЪ[12 ├Ч 10 ├Ч 8 ├Ч 6]┬а = тИЪ5760 = 75.89 cm┬▓ тЙИ 76 cm┬▓. Correct answer: c) 76 cm┬▓

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