To answer this question we will use the following equations:
[tex]\begin{gathered} Circumference=2\pi r, \\ Area=\pi r^2. \end{gathered}[/tex]Since the circular plate has a circumference of 33.9in, then we can set the following equation:
[tex]33.9in=2\pi r.[/tex]Dividing the above equation by 2π we get:
[tex]\begin{gathered} \frac{33.9in}{2\pi}=\frac{2\pi r}{2\pi}, \\ r\approx5.398in. \end{gathered}[/tex]Substituting r=5.398in in the second formula we get:
[tex]\begin{gathered} Area=\pi *(5.398in)^2 \\ \approx91.494in^2\approx91in^2. \end{gathered}[/tex]Answer:
[tex]91in^2.[/tex]