Chapter 8.3, Problem 34E

Regular octagon ABCDEFGH is inscribed in a circle whose radius is $\frac{7}{2}\sqrt{2}$ cm. Considering that the area of the octagon is less than the area of the circle and greater than the area of the square ACEG, find the two integers between which the area of the octagon must lie.

(Note: For the circle, use $A=\pi r^2$ with $\pi \approx \frac{22}{7}$.)