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Math Help - hexagon

  1. #1
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    hexagon



    hi can someone please explain the solution to me please, thanks
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  2. #2
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    Re: hexagon

    Do you want us to find and explain the solution? Or just explain the solution without giving the solution? Where has your working taken you so far?
    Thanks from topsquark
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  3. #3
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    Re: hexagon

    I just would like and explanation please
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  4. #4
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    Re: hexagon

    hexagon-02-dec-2013.png with this much you should be able to complete
    Thanks from vegasgunner and HallsofIvy
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  5. #5
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    Re: hexagon

    Quote Originally Posted by ibdutt View Post
    Click image for larger version. 

Name:	02 Dec 2013.png 
Views:	10 
Size:	35.4 KB 
ID:	29839 with this much you should be able to complete
    thank you I have solved it to be 4/3
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  6. #6
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    Re: hexagon

    Good! I presume that you realized from idbutt's picture that the if we take the distance from the center to a vertex of the outer hexagon to be 1, then the distance from the center to the middle of a side of that hexagon is \sqrt{3}/2. And that is where the circle touches the hexagon so is a vertex of the inner hexagon. Since those are "equivalent" distances, the ratio of the areas is the square of the ratio of those distances: \left(\frac{1}{\sqrt{3}/2}\right)^2= \frac{1}{3/4}= \frac{4}{3}.
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