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Math Help - Geometry

  1. #1
    Junior Member
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    Aug 2008
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    Geometry

    I attatched a figure on dot paper.
    I am to divide the region into three congruent parts, but I have no idea how to do this with this strange shape. Thank you all for your time and help.

    The picture is a 4 by 4 square with one unit cut out of the bottom right hand corner.

    Click on the picture for an enlarged copy of it.
    Attached Thumbnails Attached Thumbnails Geometry-question-23.bmp  
    Last edited by Rocker1414; September 1st 2008 at 01:16 PM.
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  2. #2
    Junior Member
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    haha nevermind came up with the answer, thanks guys
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  3. #3
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    Hello, Rocker1414!

    I'm delighted that you solved it.

    It can be solved with a bit of Thinking.
    Code:
          *---*---*---*---*
          |   :   :   :   |
          * - + - + - + - *
          |   :   :   :   |
          * - + - + - + - *
          |   :   :   :   |
          * - + - + - *---* 
          |   :   :   |
          *---*---*---*

    We have 15 unit squares, to be divided into three congruent groups.
    Hence, each group contains 5 units squares.

    There are 12 possible shapes ("Pentominos"),
    . . but only one can be used to fill the board.

    And there is basically one solution.
    Code:
          *-----------*---*
          |           |   |
          |       *---*   |
          |       |       |
          *-------*       |
          |       |       |
          |       *---*---* 
          |           |
          *-----------*
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