SOLUTION
Step 1:
The area of the shaded figure =
Area of the square - area of the circle
Step 2: Find the area of the square
[tex]\begin{gathered} \text{Area = l}^2 \\ \text{Where l = length of the square.} \end{gathered}[/tex]To find the length of the square, we have to use the diameter of the circle.
The diameter of the circle d:
[tex]\begin{gathered} d=2r \\ d=2(12\operatorname{cm}) \\ d=24\operatorname{cm}\text{.} \end{gathered}[/tex]The diameter of the circle is also the length of the outer square.
Therefore length of square (l) = diameter of circle = 24cm
Area of square
[tex]\begin{gathered} \text{Area of square=l}^2 \\ =(24cm)^2 \\ =576cm^2 \end{gathered}[/tex]Step 3: Find the area of the circle
[tex]\begin{gathered} \text{Area of circle = }\pi r^2 \\ \text{Where }\pi=3.14 \\ r=\text{radius}=\text{ 12cm} \\ Area\text{ = 3.14 (12cm)}^2 \\ =3.14\times144\operatorname{cm} \\ =452.16cm^2 \end{gathered}[/tex]Step 4: Find the area of the shaded figure.
The area of the shaded figure =
Area of the square - area of the circle
The area of the shaded figure =
[tex]\begin{gathered} 576cm^2-452.16cm^2 \\ =123.84cm^2 \end{gathered}[/tex]Conclusion: The area of the shaded figure is
[tex]123.84cm^2[/tex]
