Don't laugh! Papercraft designer needs help!

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inkinmama

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Aug 7, 2007
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I have been out of school waaaaay too long! I am making a handmade book, and I need to be able to construct a pentagon inside a circle that is 28" in diameter. What would the measurement of the side of the pentagon end up being?

Thanks!
 
If the diameter of your circle is 28", then the radius is 14".

Therefore, the length of a side of the pentagon is

\(\displaystyle \L\\28sin(36)=16.46\) inches.

About 16 and 1/2 inches would be close.

We find the length of S and multiply by 2.

penttx2.gif
 
each side of the pentagon = 2r*sin(36) = 28*sin(36) = 16.45798706"

the big question is ... how accurate can you measure?
 
If you tell us a little more about why do you want to construct such a pentagon - we might be able to help you more regarding how - like how accurate do you need to be to draw such pentagon.
 
Thanks everyone! So basically, the formula I'd follow for any size book I'm making is 2r*sin(36), correct? I don't need to be dead-on accurate, I just need to be close. The pentagon side is actually a piece of paper that is attached between the pages of the book , so that it "pops out" when the book is opened. In order for it to work it needs to be a little longer than the side of the pentagon. I thought it would be much easier to apply a little geometry, then to keep cutting up paper and trying to guess! I'll post a link to pics of the book when I'm done, if anyone wants to see their math in action!

Thanks so much!! :D
 
While we're on the topic, is there anyway to do the same thing with a heptagon? Would I use the sine of 52?

Thanks!
 
Actually, it would be \(\displaystyle \L\\sin(\frac{360}{14})\)

You divide 360 by twice the number of sides.

You could also use the law of cosines to find the side length.

Hence, deriving the general formula, knowing the radius (r) and number of sides of your n-gon (n):

\(\displaystyle \L\\r\sqrt{2(1-cos(\frac{360}{n}))}\)

Go ahead and give it a whirl. If you enter in r=14 and n=5, as from your last problem, you get 16.46

If you enter in r=14 and n=7(heptagon), you get 12.15
 
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