Answer:
\(42.1\text{ cm}^2\)
Step-by-step explanation:
We can model the area of the shaded region as:
\(A_{\rm shaded} = A_{\rm square} - A_{\rm circle}\)
We know the following area formulas:
- \(A_\text{square} = s^2\)
- \(A_\text{circle} = \pi r^2\)
We know the following lengths:
- \(s = 14\text{ cm}\)
- \(r = s/2 = 14/2 = 7\text{ cm}\)
Plugging these into the area of the shaded region equation:
\(A_{\rm shaded} = s^2 - \pi r^2\)
\(A_{\rm shaded} = (14\text{ cm})^2 - \pi(7\text{ cm})^2\)
\(\boxed{A_{\text{shaded}} \approx 42.1\text{ cm}^2}\)
