jmc

Draw horizontal diameters of both circles to form two rectangles, both surrounding shaded regions. The height of each rectangle is a radius and the length is a diameter, so the left rectangle is 2 ft $\times$ 4 ft and the right rectangle is 4 ft $\times$ 8 ft. The shaded region is obtained by subtracting respective semicircles from each rectangle, so the total area of the shaded region in square feet is $A=[(2)(4)-\frac{1}{2}\pi \cdot (2{)}^2]+[(4)(8)-\frac{1}{2}\pi \cdot (4{)}^2]=40-10\pi \approx \boxed{8.6}$.

Equivalently, we could notice that since the right side of the figure is scaled up from the left side by a factor of 2, areas will be scaled by a factor of $2^2=4$, and the right shaded region will be 4 times the size of the left shaded region. Then $A=5[(2)(4)-\frac{1}{2}\pi \cdot (2{)}^2],$ giving the same result.