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Math Help - Simple Geometry

  1. #1
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    Question Simple Geometry

    guys im stuck at this simple question.... but im stuck

    4 identical sectors with radius 12cm are drawn inside a square.
    find the shaded area.

    please help. a lot of thx.

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  2. #2
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    Quote Originally Posted by coolabear View Post
    guys im stuck at this simple question.... but im stuck

    4 identical sectors with radius 12cm are drawn inside a square.
    find the shaded area.

    please help. a lot of thx.
    I've modified your drawing a little bit:

    1. Use the blue right triangle to calculate the diagonal of the inner square.

    2. The area marked red is the difference between a sector (r = 12, \phi = 30^\circ) and an isosceles triangle.
    Attached Thumbnails Attached Thumbnails Simple Geometry-crosssection.gif  
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  3. #3
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    additional information

    My result:

    A=\frac12 \left(12(\sqrt{3} - 1) \right)^2 + 4 \cdot (12 \pi -36)

    But check my arithmetic!
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