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Lethal
 3 years ago
Geometry question w/ a Circle. find area of a shaded region. (Harder problem)
Lethal
 3 years ago
Geometry question w/ a Circle. find area of a shaded region. (Harder problem)

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Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0I 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.

alexwee123
 3 years ago
Best ResponseYou've already chosen the best response.1i did it a different way...

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0well. it shouldn't be that complicated im only doing geometry.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1Area of minor segment \[A = \frac{1}{2} r^2 \left(\theta\sin\theta\right) \] But the only problem is \(r\) is not given..

Hero
 3 years ago
Best ResponseYou've already chosen the best response.0I think I meant to post the area of a sector of a circle

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0you guys are thinking too hard its only like subtracting a sector

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1Area of sector  area of triangle

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1But \(r\) is not given!!! Im thinking of using the cosine rule and sine rule to find \(r\) would it work?

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0here ill take it a bit further. dw:1345780578744:dw does that help?

Hero
 3 years ago
Best ResponseYou've already chosen the best response.0It will not be hard to find \(r\)

Hero
 3 years ago
Best ResponseYou've already chosen the best response.0Is the vertex of angle 120 is the center of the circle?

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1345780720301:dw looks like you can use the sine rule..

Hero
 3 years ago
Best ResponseYou've already chosen the best response.0Okay, so yeah just do Area of Sector  Area of Triangle like what @Mimi_x3 suggested

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0soo 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.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1I got 8 as well using the sine rule

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1Now its easy..you can do it yourself

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0ok so 64 pi is the area of the circle

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0and the area of the triangle left side is 1/2 * 4sqroot3 * 4

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0*2 to make up for the other side.

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1I will just use this formula\[A = \frac{1}{2} r^2 \left(\theta\sin\theta\right) \] No need to derive it

Mimi_x3
 3 years ago
Best ResponseYou've already chosen the best response.1and it must be in radians..so convert it..

alexwee123
 3 years ago
Best ResponseYou've already chosen the best response.1you guys are thinking too hard o.0

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0oh 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

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.01/2 4sqrt3 * 4 or 8sqrt3 * 2 for the other side

alexwee123
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1345781211630:dw dw:1345781273195:dw

alexwee123
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1345781325118:dw

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0so the final answer is \[64\pi/3  16\sqrt{3}\]

alexwee123
 3 years ago
Best ResponseYou've already chosen the best response.1yes good job @Lethal

Lethal
 3 years ago
Best ResponseYou've already chosen the best response.0yep, i would best response both of u but i can only do one. thx alex.
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