Question

What is the area of the shaded region?​

Answer 1

`\large \boxed{\text{21.86 ft}^(2)}`

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

`\begin{array}{rcl}A & = & \mathbf{\left(36 - (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 $\large \boxed{\textbf{21.86 ft}^{\mathbf{2}}}$}`