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        riddles >> medium >> Find area of 22224444 octagon
        
(Message started by: Aryabhatta on Apr 1^st, 2009, 10:33am)

Title: Find area of 22224444 octagon
Post by Aryabhatta on Apr 1^st, 2009, 10:33am

Find the area of a polygon with sides 4,4,4,4,2,2,2,2 inscribed in a circle.

(See attached image).

Title: Re: Find area of 22224444 octagon
Post by towr on Apr 1^st, 2009, 11:16am

~~If I could solve [hide]8 atan(1/r) + 8 atan(2/r) = 2 pi[/hide] 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 [hide]arcsin[/hide], rather than [hide]arctan[/hide].
But the easy way is to [hide]rearrange the segments to form a square with the corners missing, which quickly gives (2 sqrt(2) + 4)² - 4 = 20 + 16 sqrt(2)[/hide]
[/edit]

Title: Re: Find area of 22224444 octagon
Post by Aryabhatta on Apr 2^nd, 2009, 8:48am

Right towr! There is an easy way and a hard way. Apparently you found both easy :P

Title: Re: Find area of 22224444 octagon
Post by towr on Apr 2^nd, 2009, 8:57am

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.