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Math Help - [SOLVED] Find the areas of the square

  1. #1
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    [SOLVED] Find the areas of the square

    Note: Figure not drawn to scale

    In the figure, what is the area of the square with the darken borders?

    page 721 #16
    Attached Thumbnails Attached Thumbnails [SOLVED] Find the areas of the square-721.jpg  
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  2. #2
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    Hello, fabxx!

    In the figure, what is the area of the inner square?
    Code:
                2        1
          *-----------*-----*
        1 |       *    *    |
          |   *         *   |
          *              *  | 2
          |*              * |
          | *              *|
        2 |  *              *
          |   *         *   |
          |    *    *       | 1
          *-----*-----------*
             1        2

    It is a square within a square.
    . . The four right triangles are congruent.

    In a right triangle, the legs are 1 and 2.
    . . Hence, the hypotenuse is \sqrt{5}

    Therefore, the area of the inner square is: . \left(\sqrt{5}\right)^2 \;=\;5 square units.

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  3. #3
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    Area of outside square=9

    Now find the area of the triangles
    they all have an area of 1
    so all triangles put together have an area of 4

    9-4=5

    the area of the inside square is 5

    instead of using pythagoras, you could just understand that the area of a right triangle is (length x height)/2
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  4. #4
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    Hello, Mike!

    An excellent solution!

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  5. #5
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    Thanks mikedwd and Soroban. You guys are great!
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