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Topic: Find area of 22224444 octagon (Read 2459 times) |
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Aryabhatta
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Find the area of a polygon with sides 4,4,4,4,2,2,2,2 inscribed in a circle.
(See attached image).
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towr
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Re: Find area of 22224444 octagon
« Reply #1 on: Apr 1st, 2009, 11:16am » |
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If I could solve 8 atan(1/r) + 8 atan(2/r) = 2 pi as quickly as quickmath, I'd happily give you the answer. But as it is, it would feel a bit like cheating.
[edit]
I wondered why a much simpler solution gave a different answer, but I got my edges wrong way around again.. Should have used arcsin, rather than arctan.
But the easy way is to rearrange the segments to form a square with the corners missing, which quickly gives (2 sqrt(2) + 4)2 - 4 = 20 + 16 sqrt(2)
[/edit]
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| « Last Edit: Apr 1st, 2009, 11:34am by towr » |
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Aryabhatta
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Re: Find area of 22224444 octagon
« Reply #2 on: Apr 2nd, 2009, 8:48am » |
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Right towr! There is an easy way and a hard way. Apparently you found both easy 
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| « Last Edit: Apr 2nd, 2009, 8:48am by Aryabhatta » |
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towr
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Re: Find area of 22224444 octagon
« Reply #3 on: Apr 2nd, 2009, 8:57am » |
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The advantage of the hard way is that it works in general for circle-circumscribed polygons. But I wouldn't know how to do it without help from a maths program or some further studying.
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