The semicircle has diameter 18 ft, so it has radius 9 ft, and this is the height of the rectangle.
The area of the shaded region is (area of rectangle) - (area of semicircle).
The area of a circle with radius [tex]r[/tex] is [tex]\pi r^2[/tex], so the area of a semicircle with the same radius is [tex]\dfrac\pi2r^2[/tex], and in this case that's [tex]\dfrac{3.14}2(8\,\mathrm{ft})^2=100.48\,\mathrm{ft}^2[/tex].
The area of the rectangle is [tex](18\,\mathrm {ft})(9\,\mathrm{ft})=162\,\mathrm {ft}^2[/tex].
Then the area of the shaded region is
[tex](162-100.48)\,\mathrm{ft}^2=61.52\,\mathrm{ft}^2[/tex]
