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Point \(Y\) lies on line segment \(\overline{XZ} \) such that \(XY = 2\) and \(YZ = 4.\) Semicircles are constructed with diameters \(\overline{XY}\)\(\overline{XZ}\), and \(\overline{YZ}\). Find the area of the blue region.

 Feb 9, 2021

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 #4
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#3 Close, but you're confusing diameter with radius.

The answer would be \(\pi\cdot \frac{1}{2}\cdot(3^2-1^2-2^2) = \pi \cdot \frac{1}{2} \cdot 4 = \boxed{2\pi}\)

 Feb 9, 2021
 #1
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The area of the blue region is pi.

 Feb 9, 2021
 #2
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That is incorrect.

faultypancake  Feb 9, 2021
 #3
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Semi circle areas are   1/ 2 pi r^2     

   calculate the largest one (r = 6)  ....and subtract the two smaller ones ( r= 2 and 4)

 

 

1/2 pi  (   6^2   - 2^2 - 4^2)

1/2 pi ( 16) = 8 π   units2

 Feb 9, 2021
 #4
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Best Answer

#3 Close, but you're confusing diameter with radius.

The answer would be \(\pi\cdot \frac{1}{2}\cdot(3^2-1^2-2^2) = \pi \cdot \frac{1}{2} \cdot 4 = \boxed{2\pi}\)

textot Feb 9, 2021
 #5
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Ooops!    My error....thanx , Textot !

Guest Feb 9, 2021
 #6
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Thank you

faultypancake  Feb 9, 2021

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