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wio Group TitleBest ResponseYou've already chosen the best response.0
Gotta remember this one theorem... something about inscribed angles and such..
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
Is that radius 6?
 one year ago

grayp Group TitleBest ResponseYou've already chosen the best response.0
actually, I don't know for sure.
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
Hmm...we cant answer the question unless we know what the radius is =/. Lets just operate assuming its 6.
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
Then the total circumference is 12pi. This tells us that the measure of angle EDN (i think thats a D in the middle) is:\[\frac{2\pi}{12\pi}\cdot 360=60\]degrees. This means that the area of that slice is:\[\frac{60}{360}\cdot \pi (6)^2=6\pi\]The same can be said of that second slice opposite EDN. So now we have to find the are of the last piece.
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
dw:1364787772939:dw
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
So we have EDN and BDA so far. 6pi each for a total of 12 pi.
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
To get the area of the last piece, we need the area of the slice ADN, minus the area of the triangle ADN.
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
Since the angle EDN is 60 degrees, it turns out that angle EAN is half of that, 30 degree (because it hits the same arc EN).
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
So now looking at that triangle (ADN), we see that:dw:1364788041228:dwthe area is going to be\[\frac{1}{2}\cdot 6\cdot 6\sin(120)=\frac {1}{2}\cdot 36\cdot \frac{\sqrt{3}}{2}=9\sqrt{3}\]
 one year ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
The area of arc ADN is:\[\frac{120}{360}\cdot \pi (6)^2=12\pi\]So the area of the region is 12pi9root(3). Putting everything together you get:\[6\pi+6\pi+12\pi9\sqrt{3}=24\pi9\sqrt{3}\]A fair warning, arithmetic may be off, check the math to make sure its correct.
 one year ago

grayp Group TitleBest ResponseYou've already chosen the best response.0
24 pi  9 root 3 is the full answer?
 one year ago
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