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## Lethal Group Title Geometry question w/ a Circle. find area of a shaded region. (Harder problem) 2 years ago 2 years ago

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1. Lethal Group Title

|dw:1345779977023:dw|

2. Lethal Group Title

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. Lethal Group Title

i am stuck from there

4. alexwee123 Group Title

i did it a different way...

5. Lethal Group Title

well explain.

6. alexwee123 Group Title

with integrals...

7. Lethal Group Title

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

8. Mimi_x3 Group Title

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 Group Title

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

10. Lethal Group Title

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

11. Mimi_x3 Group Title

Area of sector - area of triangle

12. Hero Group Title

Yeah that

13. Mimi_x3 Group Title

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

14. Lethal Group Title

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

15. Hero Group Title

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

16. Hero Group Title

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

17. Lethal Group Title

yep

18. Mimi_x3 Group Title

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

19. Hero Group Title

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

20. Lethal Group Title

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 Group Title

lets find $$r$$ first

22. Lethal Group Title

|dw:1345780842471:dw|

23. Mimi_x3 Group Title

I got 8 as well using the sine rule

24. Mimi_x3 Group Title

Now its easy..you can do it yourself

25. Lethal Group Title

ok so 64 pi is the area of the circle

26. Lethal Group Title

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

27. Lethal Group Title

*2 to make up for the other side.

28. Mimi_x3 Group Title

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

29. Lethal Group Title

ok

30. Mimi_x3 Group Title

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

31. Lethal Group Title

oh heck nah jose

32. alexwee123 Group Title

you guys are thinking too hard o.0

33. Lethal Group Title

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. Lethal Group Title

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

35. alexwee123 Group Title

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

36. alexwee123 Group Title

|dw:1345781325118:dw|

37. Lethal Group Title

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

38. alexwee123 Group Title

yes good job @Lethal

39. Lethal Group Title

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