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Math Help - Nonagon

  1. #1
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    What is the area of a Nonagon if the radius is 8 in. Answer must be rounded to the nearest tenth.

    Here is some of my work.
    I found a formula online that could help. It was nr^2tan(180/n) where n=number of sides and r=radius

    If that is the case, I got 576(tan20) as an answer, which equals 1288.6 rounded......I have doubts to that answer....

    Am I right or wrong....Any help is greatly appreciated....

    Is there a possible generalization to this too? (for any # sided polygon)
    Last edited by mr fantastic; May 18th 2010 at 07:50 PM. Reason: Merged posts.
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  2. #2
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    Quote Originally Posted by BrendanLoftus View Post
    What is the area of a Nonagon if the radius is 8 in. Answer must be rounded to the nearest tenth.

    Here is some of my work.
    I found a formula online that could help. It was nr^2tan(180/n) where n=number of sides and r=radius

    If that is the case, I got 576(tan20) as an answer, which equals 1288.6 <<<<<< how did you get this result?
    rounded......I have doubts to that answer....

    Am I right or wrong....Any help is greatly appreciated....

    Is there a possible generalization to this too? (for any # sided polygon)
    1. I assume that you mean a regular nonagon ....?

    2. You didn't mention if "the radius" belongs to the incircle of the nonagon or the circumscribed circle.

    3. The formula you used gives the area of a regular nonagon with an incircle of r = 8.

    4. To derive a general formula to calculate the area consider a regular n-gon as n isosceles congruent triangles. You can calculate the base and the height of one triangle using the radius of the circle.

    5. Btw 576\cdot \tan(20^\circ)\approx 209.65
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