Question 177346
since the square is inscribed in the circle, then all 4 points of the square lie on the circle.
since the diagonals of a square are equal to each other, then each diagonal must be a diameter of the circle and they must pass through the center of the circle.
since the area of the square is 64 square inches, then each side of the square musts be 8 inches since 8*8 = 64
since each side of the square is 8 inches, then the diagonal of the square must be {{{sqrt(8^2+8^2) = sqrt(128) = 11.3137085}}}.
since the diagonal of the square is also the diameter of the circle, this means that the radius of the circle must be 1/2 * 11.3137085 = 5.65685425.
this means that the area of the circle is pi*(5.65685425)^2 = 100.5309649.
can't go any further with this because i don't know what the shaded region is.
if the shaded region is the area of the circle outside the square, then the area of the shaded region is the area of the circle minus the area of the square.
if the shaded region is the area of the circle outside the square, but only one of the 4 sections, then the area of that shaded region is one fourth times the (area of the circle minus the area of the square).
hopefully this will help you get started at least.