Answer:Part a) The area of the shaded region is [tex]41\ ft^{2}[/tex]Part b) The area of the nonshaded region is [tex]87\ ft^{2}[/tex]Step-by-step explanation:we know thatThe total area is equal to the area of the shaded region plus the area of the nonshaded regionstep 1Find the total area The total area is equal to the area of the rectangle[tex]A=8(16)=128\ ft^{2}[/tex]step 2Find the area of the shaded regionThe area of the shaded region is equal to the area of the trapezoid minus the area of the smaller squareso[tex]A=\frac{1}{2}[(8-2)+3)](8+2) -2^{2} \\ \\A=\frac{1}{2}[9](10) -4\\ \\A=41\ ft^{2}[/tex]step 3Find the area of the nonshaded regionThe area of the nonshaded region is equal to the total area minus the area of the shaded regionso[tex]A=128\ ft^{2}-41\ ft^{2}=87\ ft^{2}[/tex]