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    Question

    In the given figure, AB, AE, EF, FG and GB are

    semicircles. AB = 56 cm and AE = EF = FG = GB. What is the area (in cm2) of the shaded region?
    A 414.46 Correct Answer Incorrect Answer
    B 382.82 Correct Answer Incorrect Answer
    C 406.48 Correct Answer Incorrect Answer
    D 394.24 Correct Answer Incorrect Answer

    Solution

    AE = EF = FG = GB = 14 Radius = 14/2 = 7 Radius of Semicircle = 7 OF = MF – MO = (28 – r) FB = MF = 28 ∠ 900, OF is targent for circle EF centre to targent 900 ∆ UPF apply PGT (7)2 + (28 – r)2 = (7 + r)2 49 = (7 + r)2 – (28 – r)2 49/7 = (35) – (2r – 21) 7 = 10r – 105 10r = 112 r = 11.2 area = πr2 = 22/7 × 11.2 × 11.2 = 394.24 cm2

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