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Cloud moderators

18/12/2017 at 09:09
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In the square shown, the side lengths are 6 cm, and the intersecting arcs are quarter-circles. The area of the shaded region, expressed in simplest radical form in terms of π, is aπ + b\(\sqrt{c}\) cm\(^2\). What is the value of a + b + c?
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    Phan Thanh Tinh Coordinator 15/01/2018 at 23:29

    A B C D E

    Since AE = BE = AB, \(\Delta ABE\) is an equilateral triangle

    \(S_{ABE}=\dfrac{6^2\sqrt{3}}{4}=9\sqrt{3}\) (cm2)

    The area of the sector ABE is : \(\dfrac{6^2\pi.60}{360}=6\pi\) (cm2)

    The area of the shaded region is :

    \(\dfrac{6^2\pi.90}{360}.2-\left[9\sqrt{3}+2\left(6\pi-9\sqrt{3}\right)\right]=6\pi+9\sqrt{3}\) (cm2)

    The answer is : 6 + 9 + 3 = 18


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