anonymous
  • anonymous
How do we find the area of a nonagon if each side is 3 cm? Please and thanks.
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Nanagon has nine sides. So, it forms 9 triangles with the center. Find the area of one of these triangles and multiply by 9.
anonymous
  • anonymous
6,18182*3^2 = 55,6364
anonymous
  • anonymous
No, it is not.

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anonymous
  • anonymous
\[area= \left( s ^{2}N \right) \div \left( 4\tan \left( 180/N \right) \right)\] Where s is the length of any side N number of sides in your case, N=9, s=0.03 meters
anonymous
  • anonymous
It is 6.18182 not 6,18182. Also, using a formula like that blindly is silly.
anonymous
  • anonymous
omar_86 - using a formula like that is also silly. Best to figure it out from the shape and triangles formed. The formula came from doing that fundamental math.
anonymous
  • anonymous
Dear GT, both ways are right...
anonymous
  • anonymous
Plugging values into a formula does not teach anyone anything.
anonymous
  • anonymous
I did it for 7-gon. Sorry. It is a 9-gon.
anonymous
  • anonymous
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anonymous
  • anonymous
|dw:1327934503376:dw|
anonymous
  • anonymous
area of triangle = 1/2 * base * height = 1/2 * 3 * 4.12 = 6.18 There are nine triangles. So, the area of Nanagon = 9 * area of each triange = 9 * 6.18 = 55.62 sq units.
anonymous
  • anonymous
Hope that helps you to figure out for ANY n-gon.
mathmate
  • mathmate
on "It is 6.18182 not 6,18182." Dear GT, Since we are international in this study forum, it may be interesting to know that there are countries which use the comma "," instead of the decimal point. So 6,18182 is written correctly in his/her region/locality. MM
anonymous
  • anonymous
all of you, thnx XD I understand it now!
anonymous
  • anonymous
btw, is there a name for the formula Omar used?
anonymous
  • anonymous
Oh yeah....Germans write it that way.
anonymous
  • anonymous
@14yamak - the formula is nothing but an extension of my calculation. Instead of using the angles I use, you need to represent them in terms of N (number of sides). You will then get the formula by yourself.
anonymous
  • anonymous
we norwegians write like that too. i'm sorry if my writing methods made some confusion

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