Given the figure shown in the picture, you can identify that there is a circle inside a square. Therefore, the area of the shaded region can be calculated by subtracting the area of the circle from the area of the square.
The formula for calculating the area of a circle is:
[tex]A_c=\pi r^2[/tex]
Where "r" is the radius of the circle.
The formula for calculating the area of a square is:
[tex]A_s=s^2[/tex]
Where "s" is the side length of the square.
Therefore, you can write the following formula for calculating the area of the shaded region:
[tex]A_{sr}=s^2-\pi r^2[/tex]
In this case, you can identify that:
[tex]\begin{gathered} s=16cm \\ \\ r=\frac{16cm}{2}=8cm \end{gathered}[/tex]
Therefore, by substituting values into the formula and evaluating, you get:
[tex]A_{sr}=(16cm)^2-\pi(8cm)^2\approx54.9cm^2[/tex]
Hence, the answer is: Last option.
