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
~~~~~~~~~~~~~~~~~~~~~~~


<pre>
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  

    {{{a^2*(sqrt(3)/4))}}} = {{{(2r)^2*(sqrt(3)/4)}}} = {{{4r^2*(sqrt(3)/4)}}} = {{{r^2*sqrt(3)}}}.


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 {{{(pi/2)r^2}}},
one half of the area of one circle.


So, the shaded are is

    {{{r^2*sqrt(3)}}} - {{{(pi/2)*r^2}}},    <U>ANSWER</U>


in terms of "r".
</pre>

Solved.