## anonymous 4 years ago How do we find the area of a nonagon if each side is 3 cm? Please and thanks.

1. 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.

2. anonymous

6,18182*3^2 = 55,6364

3. anonymous

No, it is not.

4. 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

5. anonymous

It is 6.18182 not 6,18182. Also, using a formula like that blindly is silly.

6. 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.

7. anonymous

Dear GT, both ways are right...

8. anonymous

Plugging values into a formula does not teach anyone anything.

9. anonymous

I did it for 7-gon. Sorry. It is a 9-gon.

10. anonymous

|dw:1327934436452:dw|

11. anonymous

|dw:1327934503376:dw|

12. 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.

13. anonymous

Hope that helps you to figure out for ANY n-gon.

14. 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

15. anonymous

all of you, thnx XD I understand it now!

16. anonymous

btw, is there a name for the formula Omar used?

17. anonymous

Oh yeah....Germans write it that way.

18. 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.

19. anonymous

we norwegians write like that too. i'm sorry if my writing methods made some confusion