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!!!

Guest May 27, 2020

#1**0 **

The inner-most circle has a radius of 2 feet so its area is: A = pi·radius^{2} = pi·2^{2} = 4·pi

The next circle has a radius of 4 feet so its area (including the smaller circle) is pi·4^{2} = 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**

geno3141 May 28, 2020