Since the inscribed polygon is an octagon, then the top angle of the small right-angle triangle=
180/8 =22.50 degrees.
Cos(22.5) = 4.5 / radius
Radius =4.5/cos(22.5)
Radius =4.87
Area of circle =4.87^2 x pi
=~74.50
Area of the octagon=sin(22.5) x 4.5 x 4.87 x 8 =~67.10
Area of the shaded region =74.5 - 67.1 =7.4