1. anonymous

Referring to the figure, find the perimeter of the regular polygon shown.

2. anonymous

|dw:1436925905126:dw|

3. anonymous

@Loser66 @Whitemonsterbunny17 @alix

4. anonymous

@AAlixH

5. anonymous

@satellite73

6. freckles

|dw:1436927827901:dw| well hmmm we know all sides are equal

7. freckles

so once we find a we can say the perimeter is a+a+a or 3a

8. anonymous

Ok...... But Idk how to find A. Is there a formula?

9. freckles

I wonder if that is suppose to represent a "radi" of the equilateral

10. freckles

do you think that 6 is suppose to represent the radius of the regular polyngon?

11. anonymous

In the original picture the number 6 is more then half or the triangle

12. freckles

I think 6 is the length of the radius of the regular tri-gon here since the other line segment there is the apothem and I know it is the apothem because it runs perpendicular to a side of the regular tri-gon

13. freckles

$radius \dot 2 \sin(\frac{180}{n})=s$

14. freckles

n represents number of sides

15. freckles

s is the side length

16. anonymous

@freckles

17. freckles

yes?

18. anonymous

180/3=60

19. freckles

yes 180 divided by 3 is 60 so you have radius*2sin(60)=s

20. anonymous

Now what do I do? Multiply the radius by itself or by 2 or what?

21. freckles

multiply the radius the 2 and the sin(60)

22. freckles

|dw:1436929098581:dw| this is how I got the formula by the way $\sin(60)=\frac{\frac{a}{2}}{6} \\ \sin(60)=\frac{a}{6 (2)} \\ 6(2) \sin(60)=a$

23. freckles

you just have to find the product of 6 and 2 and sin(60) you can use a calculator if you want

24. anonymous

So I have to find the sin of 60

25. freckles

yes you have to compute 6 times 2 times sin(60)

26. freckles

6*times 2 is 12 so 12*sin(60) gives you what ?

27. freckles

are you having trouble doing this ?

28. freckles

you could put sin(60) in a calculator or if you learned any unit circle stuff you can find sin(60) exactly on the unit circle

29. freckles

there is also another way I can derive it for you |dw:1436929558610:dw| use Pythagorean theorem to find the height

30. freckles

$2^2=h^2+1^2 \\ 4=h^2+1 \\ 3=h^2 \\ \sqrt{3}=h$

31. freckles

|dw:1436929645603:dw|

32. freckles

$\sin(60)=\frac{opp}{hyp}=\frac{\sqrt{3}}{2}$

33. anonymous

@freckles

34. anonymous

35. freckles

I don't know I would have to find a calculator and do 12*sqrt(3)/2 aka 6*sqrt(3) $6\sqrt{1} < 6 \sqrt{3} <6 \sqrt{4} \\ 6<6 \sqrt{3}<6(2) \\ 6 <6 \sqrt{3}<12$ so it seems like you are in the ball park the number is between 6 and 12 and probably a bit closer to 12 than 6 ...but let me get a calculator to approximate 6sqrt(3)

36. freckles

yes 6 sqrt(3) is 10.39 approximately

37. anonymous

@freckles thank you 0p