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# Help Asap. please and thank you

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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

#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
+165
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#3 Close, but you're confusing diameter with radius.

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

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

Guest Feb 9, 2021
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Thank you

faultypancake  Feb 9, 2021