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## anonymous 4 years ago Geometry question w/ a Circle. find area of a shaded region. (Harder problem)

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1. anonymous

|dw:1345779977023:dw|

2. anonymous

I think what you have to do is to bisect the triangle into 60 degree up top and then the bottom left and right are still 30 degrees. then you do the 30 60 90 triangle thing.

3. anonymous

i am stuck from there

4. alexwee123

i did it a different way...

5. anonymous

well explain.

6. alexwee123

with integrals...

7. anonymous

well. it shouldn't be that complicated im only doing geometry.

8. Mimi_x3

Area of minor segment $A = \frac{1}{2} r^2 \left(\theta-\sin\theta\right)$ But the only problem is $$r$$ is not given..

9. Hero

I think I meant to post the area of a sector of a circle

10. anonymous

you guys are thinking too hard its only like subtracting a sector

11. Mimi_x3

Area of sector - area of triangle

12. Hero

Yeah that

13. Mimi_x3

But $$r$$ is not given!!! Im thinking of using the cosine rule and sine rule to find $$r$$ would it work?

14. anonymous

here ill take it a bit further. |dw:1345780578744:dw| does that help?

15. Hero

It will not be hard to find $$r$$

16. Hero

Is the vertex of angle 120 is the center of the circle?

17. anonymous

yep

18. Mimi_x3

|dw:1345780720301:dw| looks like you can use the sine rule..

19. Hero

Okay, so yeah just do Area of Sector - Area of Triangle like what @Mimi_x3 suggested

20. anonymous

soo all we need is the area of the circle and then we can use the 120/360 * pi r2 or something and subtract the area from that.

21. Mimi_x3

lets find $$r$$ first

22. anonymous

|dw:1345780842471:dw|

23. Mimi_x3

I got 8 as well using the sine rule

24. Mimi_x3

Now its easy..you can do it yourself

25. anonymous

ok so 64 pi is the area of the circle

26. anonymous

and the area of the triangle left side is 1/2 * 4sqroot3 * 4

27. anonymous

*2 to make up for the other side.

28. Mimi_x3

I will just use this formula$A = \frac{1}{2} r^2 \left(\theta-\sin\theta\right)$ No need to derive it

29. anonymous

ok

30. Mimi_x3

and it must be in radians..so convert it..

31. anonymous

oh heck nah jose

32. alexwee123

you guys are thinking too hard o.0

33. anonymous

oh wait i got the answer. just do 120/360 which is 1/3 and then i did 1/3 * 64pi which is the area of the circle and it is 64pi/3 and now subtract it by the area of the triangle which is

34. anonymous

1/2 4sqrt3 * 4 or 8sqrt3 * 2 for the other side

35. alexwee123

|dw:1345781211630:dw| |dw:1345781273195:dw|

36. alexwee123

|dw:1345781325118:dw|

37. anonymous

so the final answer is $64\pi/3 - 16\sqrt{3}$

38. alexwee123

yes good job @Lethal

39. anonymous

yep, i would best response both of u but i can only do one. thx alex.

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