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  1. #1

    geometry question area

    In the figure below the triangle DGF has an area of 12 and DG=GF, what is the area of the shaded region?

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    Figure not drawn to scale


    (A)

    (B)

    (C)

    (D)


    Thanks

  2. #2
    The triangle DGF is equilateral since DG=DF as radii and we also know that DG=GF.
    Therefore, each angle of the triangle DGF measures .
    We’ ll use two formulas for areas.

    The first one gives us the area of triangle in terms of any two sides and their included angle





    and the other gives us the area of a sector in terms of radius and the central angle (in radians!!) of the sector




    So, the area of the shaded region is given by the following expression



    Therefore the correct answer is (D).

    Hope these help!
    Last edited by miranda; 10-10-2013 at 12:39 PM.

  3. #3
    Thanks miranda!!

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