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A decorative arrangement of floor tiles forms concentric circles, as shown in the figure to the right. The smallest circle has a radius of 2 feet, and each successive circle has a radius 2 feet longer. All the lines shown intersect at the center and form 12 congruent central angles. What is the area of the shaded region? Express your answer in terms of π .  Thank you!!!

 

 

 May 27, 2020
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The inner-most circle has a radius of 2 feet so its area is:  A  =  pi·radius2  =  pi·22  =  4·pi

The next circle has a radius of 4 feet so its area (including the smaller circle) is  pi·42  =  16·pi

 

The area of the whole second band is:  16·pi  -  4·pi  =  12·pi

 

But this is the area of the whole band, just the one section is  12·pi / 12  =  pi

 May 28, 2020

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