Answer:
[tex]\large \boxed{\text{21.86 ft}^{2}}[/tex]
Step-by-step explanation:
Area of shaded region = area of square - area of semicircle
1. Area of square
A = s² = (6 ft)² = 36 ft²
2. Area of semicircle
Area of circle = πr²
Area of semicircle = ½πr²
r = 3 ft, so
A = ½π(3 ft)² = ⁹/₂π ft³
3. Area of shaded region
A = area of square - area of semicircle
[tex]\begin{array}{rcl}A & = & \mathbf{\left(36 - \dfrac{9}{2} \pi \right )} \textbf{ ft}^{\mathbf{2}}\\\\ &\approx & \left (36 - 14.1372\right)\text{ ft}^{2}\\ & \approx & \mathbf{21.86}\textbf{ ft}^{\mathbf{2}} \\\end{array}\\\text{The area of the shaded figure is approximately $\large \boxed{\textbf{21.86 ft}^{\mathbf{2}}}$}[/tex]
