Question 1199144
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The centers of the circles form an equilateral triangle with the side a = 5+5 = 10 inches.


The area of this triangle is  A = {{{a^2*(sqrt(3)/4)}}} = {{{10^2*sqrt(3)/4)}}}.


Each circular sector of interest has the area of  {{{1/6}}}  of the area of the circle of radius 10 inches.


So we need to subtract  {{{3*(1/6)*pi*r^2}}} = {{{(1/2)*3.14*(sqrt(3)/4)}}} from A:


    the area of interest is  {{{a^2*(sqrt(3)/4)}}} - {{{(1/2)*pi*r^2}}}  (exact formula).


Substitute the numbers and calculate using your calculator.
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Solved.