Question 461955
The diagonal of the square is {{{6sqrt(2)}}} inches, since an edge is 6 inches long.  The radius of the circle is then half of this, or {{{3sqrt(2)}}} inches.  Hence the area of the circle is {{{A = (3sqrt(2))^2*pi = 18pi}}} square inches.  The area of the square is 36 square inches.
The area of one segment, by symmetry, is a quarter of the difference between the area of the circle and the area of the inscribed square, or

{{{(18pi - 36)/4 = (9pi - 18)/2}}} square inches.