Answer: [tex]119.43\ cm^2[/tex]
Step-by-step explanation:
The area of the rectangle can be calculated with the following formula:
[tex]A_r=lw[/tex]
Where "l" is the length and "w" is the width.
In this case:
[tex]l=12\ cm\\w=11\ cm[/tex]
Then, substituting values into the formula, you get that the area of the rectangle shown in the figure is:
[tex]A_r=(12\ cm)(11\ cm)\\\\A_r=132\ cm^2[/tex]
The formula that is used to find the area of a circle is:
[tex]A_c=\pi r^2[/tex]
Where "r" is the radius of the circle.
In this case you know that:
[tex]r=2\ cm[/tex]
Then, the area of the given circle is:
[tex]A_c=\pi (2\ cm)^2\\\\A_c=12.566\ cm^2[/tex]
Subtract both areas in order to find the area of the shaded region. Rounded to the nearest hundredth, this is:
[tex]A_s=132\ cm^2-12.566\ cm^2\\\\A_s=119.43\ cm^2[/tex]
