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Math Help - Geometry

  1. #1
    Newbie
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    Geometry

    Hi,
    Okay i am stuck on this problem. There is a square with four congruent quarter circles in it, each with a radius of four. In the middle of the square there is a shaded region that resembles a curved diamond shape, which i am supposed to find the area of.

    Thanks for any help
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  2. #2
    Super Member

    Joined
    May 2006
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    Lexington, MA (USA)
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    Hello, Softballgrl!

    There is a square with four congruent quarter circles in it,
    each with a radius of four. In the middle of the square there is a shaded region
    that resembles a curved diamond shape, which i am supposed to find the area of.
    Code:
               4         4
          * - - - - * - - - - *
          |         *         |
          |         :         |
        4 |        *:*        |
          |       *:::*       |
          |     *:::::::*     |
          * *:::::::::::::::* * 8
          |     *:::::::*     |
          |       *:::*       |
        4 |        *:*        |
          |         :         |
          |         *         |
          * - - - - * - - - - *
                    8

    The square has an area of: . 8^2\:=\:64 square units.

    The four quarter-circles comprise one circle with radius 4.
    . . Its area is: . \pi r^2\:=\:16\pi square units.

    Therefore, the shaded region has an area of (64 - 16\pi) square units.

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