SOLUTION: Find the area of the shaded region in terms of r if each circle has radius r. Link to graph: https://ibb.co/9Yd5Nsh

Question 1209479: Find the area of the shaded region in terms of r if each circle has radius r.
Link to graph: https://ibb.co/9Yd5Nsh
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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Find the area of the shaded region in terms of r if each circle has radius r.
Link to graph: https://ibb.co/9Yd5Nsh
~~~~~~~~~~~~~~~~~~~~~~~

Consider the triangle, formed by the three centers of the circles.


This triangle is equilateral with the side length a = 2r.


The area of this triangle is  

     =  =  = .


To get the shaded area, we should subtract the areas of 3 sectors of the radius r,
each with the central angle of 60 degrees. These three segments together have the area ,
one half of the area of one circle.


So, the shaded are is

     - ,    ANSWER


in terms of "r".

Solved.

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