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