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Math Help - area of shaded

  1. #1
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    area of shaded

    The circle has radius of 5 cm.
    the square of ABC is placed inside the circle and part of it shaded.
    lets find the area of shaded region
    Attached Thumbnails Attached Thumbnails area of shaded-square.jpg  
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  2. #2
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by janeyandtaz View Post
    The circle has radius of 5 cm.
    the square of ABC is placed inside the circle and part of it shaded.
    lets find the area of shaded region
    The diagonal of the big square is 10cm because that's the diameter of the circle.

    So the big square has side length \frac {10}{\sqrt 2} = 5 \sqrt 2.

    That's the same length as the diagonal of the small square. So you can work out the side length of the small square, and so square that to get its area.
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  3. #3
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    Hello, janeyandtaz!

    The circle has radius of 5 cm.
    The square ABCD is placed inside the circle and part of it shaded.
    Find the area of shaded region.
    Code:
                  * * *
              *      P    *
          A o - - - o - - - o B
           *|     *:::*     |*
            |   *:::::::*   |
         *  | *:::::::::::* |  *
         *  *:::::::::::::::oQ *
         *  | *:::::::::::* |  *
            |   *:::::::*   |
           *|     *:::*     |*
          D o - - - * - - - o C
              *           *
                  * * *

    The diagonal of the large square AC equals the diameter: 10 cm.

    In triangle ABC,\;PQ joins the midpoints of two sides.
    Hence, it is half the length of the third side AC.

    So the side of the small square PQ is 5 cm.


    Therefore, the area of the small square is: . 5^2 \,=\,25\text{ cm}^2

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  4. #4
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    Thumbs up

    Hi yaa...

    Soroban, u got it exactly
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  5. #5
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by janeyandtaz View Post
    Hi yaaaa...
    Soroban, u got it rite!
    D'oh! didn't I, then?
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