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Math Help - Circumscribed/inscribed area problem

  1. #1
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    Circumscribed/inscribed area problem

    I've attached the homework problem I'm having.

    My biggest issue is getting it into sigma notation to use the summation rules on it. At least I think that's where my failure is.

    I really need to see this or a similar problem worked out entirely using sigma notation. The homework does not use sigma notation but instead does it manually, but this is not what the instructor wants us to do.

    Thanks.
    Attached Thumbnails Attached Thumbnails Circumscribed/inscribed area problem-circumscribed-polygon.jpg  
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  2. #2
    MHF Contributor
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    Hi

    The area of the first rectangle is 1 \cdot f\left(\frac12\right)

    The area of the second rectangle is 1 \cdot  f\left(1\right)

    and so on

    The area of the polygon is 1 \cdot \sum_{k=1}^{4} f\left(\frac{k}{2}\right)
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  3. #3
    MHF Contributor
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    Thanks
    1
    As the base of the rectangles is \frac{1}{2}

    we need to multiply y by 0.5

    However, the answer given is the sum of the areas of the first 5 rectangles.

    \frac{1}{2}\sum_{k=1}^5f\left(k\right)=\frac{1}{2}  \left(8+\frac{1}{8}+8+\frac{4}{8}+8+\frac{9}{8}+8+  \frac{16}{8}+8+\frac{25}{8}\right)=\frac{375}{16}=  \frac{46.8}{2}
    Last edited by Archie Meade; April 15th 2010 at 12:10 PM.
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