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MEDAL AND FAN!!!!! PLEASE HELP!!!!!

Mathematics
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Referring to the figure, find the perimeter of the regular polygon shown.
|dw:1436925905126:dw|

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|dw:1436927827901:dw| well hmmm we know all sides are equal
so once we find a we can say the perimeter is a+a+a or 3a
Ok...... But Idk how to find A. Is there a formula?
I wonder if that is suppose to represent a "radi" of the equilateral
do you think that 6 is suppose to represent the radius of the regular polyngon?
In the original picture the number 6 is more then half or the triangle
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
\[radius \dot 2 \sin(\frac{180}{n})=s\]
n represents number of sides
s is the side length
yes?
180/3=60
yes 180 divided by 3 is 60 so you have radius*2sin(60)=s
Now what do I do? Multiply the radius by itself or by 2 or what?
multiply the radius the 2 and the sin(60)
|dw:1436929098581:dw| this is how I got the formula by the way \[\sin(60)=\frac{\frac{a}{2}}{6} \\ \sin(60)=\frac{a}{6 (2)} \\ 6(2) \sin(60)=a\]
you just have to find the product of 6 and 2 and sin(60) you can use a calculator if you want
So I have to find the sin of 60
yes you have to compute 6 times 2 times sin(60)
6*times 2 is 12 so 12*sin(60) gives you what ?
are you having trouble doing this ?
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
there is also another way I can derive it for you |dw:1436929558610:dw| use Pythagorean theorem to find the height
\[2^2=h^2+1^2 \\ 4=h^2+1 \\ 3=h^2 \\ \sqrt{3}=h\]
|dw:1436929645603:dw|
\[\sin(60)=\frac{opp}{hyp}=\frac{\sqrt{3}}{2}\]
Is the answer 10.39
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)
yes 6 sqrt(3) is 10.39 approximately
@freckles thank you 0p

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