Explanation
We can find the area of the rectangle and then subtract the area of the semicircle.
[tex]A=A1-A2[/tex]
Finding the area of the rectangle
The formula to find the area of a rectangle is:
[tex]A_{rectangle}=\text{ length * width}[/tex]
Then, we have:
[tex]\begin{gathered} A1=34in*22in \\ A1=748in^2 \end{gathered}[/tex]
Finding the area of the semicircle
The formula to find the area of a semicircle is:
[tex]\begin{gathered} A_{\text{ semicircle}}=\frac{\pi r^2}{2} \\ \text{ Where } \\ r\text{ is the radius of the circle} \end{gathered}[/tex]
The radius is half of the circle. Then, the radius of the circle is 11 in.
[tex]\begin{gathered} \text{ radius }=\frac{\text{ diameter}}{2} \\ \text{rad}\imaginaryI\text{us}=\frac{22in}{2} \\ \text{rad}\imaginaryI\text{us}=11in \end{gathered}[/tex]
Then, the area of the semicircle is:
[tex]\begin{gathered} A2=\frac{\pi r^{2}}{2} \\ A2=\frac{\pi(11in)^2}{2} \\ A2=\frac{121\pi\imaginaryI n^2}{2} \\ A2=60.5\pi\imaginaryI n^2 \end{gathered}[/tex]
Calculating the area of the paperboard that remains
[tex]\begin{gathered} A=A1-A2 \\ A=748in^2-60.5\pi in^2 \\ A=557.93in^2 \end{gathered}[/tex]Answer
The area of the paperboard that remains rounding to the nearest hundredth is 557.93 in².
