The area of a regular octagon with side a is `a^2*(2 + 2*sqrt 2)` . The side a of the octagon in the figure is 6.2 cm. The area of the octagon is `6.2^2*(2 + 2*sqrt 2)` .
The line perpendicular to the side with length 7.5 cm divides it into two halves of 3.1 cm. If r is the radius of the circle, `r^2 = sqrt(7.5^2 + 3.1^2)` . The area of the circle is `pi*(65.86)`
From the area of the octagon and that of the circle the area of the shaded region is equal to: `65.86*pi - 6.2^2*(2 + 2*sqrt 2) = 21.3` cm^2
The required area of the shaded region is 21.3 cm^2