anonymous
  • anonymous
Complicated Math Question.....
Mathematics
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anonymous
  • anonymous
Complicated Math Question.....
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
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anonymous
  • anonymous
Gotta remember this one theorem... something about inscribed angles and such..
anonymous
  • anonymous
Is that radius 6?

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anonymous
  • anonymous
actually, I don't know for sure.
anonymous
  • anonymous
Hmm...we cant answer the question unless we know what the radius is =/. Lets just operate assuming its 6.
anonymous
  • anonymous
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.
anonymous
  • anonymous
|dw:1364787772939:dw|
anonymous
  • anonymous
So we have EDN and BDA so far. 6pi each for a total of 12 pi.
anonymous
  • anonymous
To get the area of the last piece, we need the area of the slice ADN, minus the area of the triangle ADN.
anonymous
  • anonymous
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).
anonymous
  • anonymous
So now looking at that triangle (ADN), we see that:|dw:1364788041228:dw|the area is going to be\[\frac{1}{2}\cdot 6\cdot 6\sin(120)=\frac {1}{2}\cdot 36\cdot \frac{\sqrt{3}}{2}=9\sqrt{3}\]
anonymous
  • anonymous
The area of arc ADN is:\[\frac{120}{360}\cdot \pi (6)^2=12\pi\]So the area of the region is 12pi-9root(3). Putting everything together you get:\[6\pi+6\pi+12\pi-9\sqrt{3}=24\pi-9\sqrt{3}\]A fair warning, arithmetic may be off, check the math to make sure its correct.
anonymous
  • anonymous
24 pi - 9 root 3 is the full answer?

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