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grayp
 2 years ago
Complicated Math Question.....
grayp
 2 years ago
Complicated Math Question.....

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wio
 2 years ago
Best ResponseYou've already chosen the best response.0Gotta remember this one theorem... something about inscribed angles and such..

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1Is that radius 6?

grayp
 2 years ago
Best ResponseYou've already chosen the best response.0actually, I don't know for sure.

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

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1Then 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.

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1364787772939:dw

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

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1To get the area of the last piece, we need the area of the slice ADN, minus the area of the triangle ADN.

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1Since 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).

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

joemath314159
 2 years ago
Best ResponseYou've already chosen the best response.1The 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.

grayp
 2 years ago
Best ResponseYou've already chosen the best response.024 pi  9 root 3 is the full answer?
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