The figure has a circle with a square inscribed in it. We are asked to find the area of the shaded portion. To find this area, we simply need to subtract the area of the square from the area of the circle.
Thus, the area of the shaded portion is given by:
[tex]\text{Area of Shaded portion = Area of Circle - Area of Square}[/tex]
Area of Circle:
[tex]\begin{gathered} \text{Area of a circle is: }\pi(\frac{d}{2})^2 \\ \\ d=3.3^{\prime} \\ \\ \therefore\text{Area of the circle }=\pi\times(\frac{3.3}{2})^2=8.553in^2 \end{gathered}[/tex]
Area of Square:
[tex]\begin{gathered} \text{Area of Square = }l^2 \\ l=2.5^{\prime} \\ \\ \therefore\text{Area of the Square }=2.5^2=6.25 \end{gathered}[/tex]
Thus, we can calculate the area of the shaded region as follows:
[tex]\begin{gathered} \text{Area of Circle - Area of Square = }8.553-6.25 \\ \therefore\text{Area of shaded region}=2.3in^2\text{ (To nearest tenth)} \end{gathered}[/tex]
The answer is 2.3 square inches
