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- Jan 26, 2012

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In the above circle the radius is 6 and chord $AB=6$. What is the area of the shaded region?

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- Thread starter
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- #1

- Jan 26, 2012

- 4,052

In the above circle the radius is 6 and chord $AB=6$. What is the area of the shaded region?

--------------------

Remember to read the POTW submission guidelines to find out how to submit your answers!

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- Jan 26, 2012

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Congratulations to the following members for their correct solutions:

1) MarkFL

2) SuperSonic4

3) soroban

4) Sudharaka

5) BAdhi

6) caffeinemachine

Solution (from soroban):

Let $O$ be the center of the circle.

The area of sector $AOB \text{ }$ is: .$\frac{1}{6}\pi r^2 \:=\:\frac{\pi}{6}(6^2) \:=\:6\pi$

The area of equilateral triangle $AOB \text{ }$ is: .$\frac{\sqrt{3}}{4}(6^2) \:=\:9\sqrt{3}$

Therefore, area of the segment is: .$6\pi - 9\sqrt{3} \;\approx\;3.261$

1) MarkFL

2) SuperSonic4

3) soroban

4) Sudharaka

5) BAdhi

6) caffeinemachine

Solution (from soroban):

The area of sector $AOB \text{ }$ is: .$\frac{1}{6}\pi r^2 \:=\:\frac{\pi}{6}(6^2) \:=\:6\pi$

The area of equilateral triangle $AOB \text{ }$ is: .$\frac{\sqrt{3}}{4}(6^2) \:=\:9\sqrt{3}$

Therefore, area of the segment is: .$6\pi - 9\sqrt{3} \;\approx\;3.261$

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