2. I'm going to assume that this plate is donut-shaped. Let $\displaystyle R = 12\,in$ and $\displaystyle r = 5\,in$. The area of this plate would be
\displaystyle \begin{aligned} A &= \pi R^2 - \pi r^2 \\ &= 12^2 \pi - 5^2 \pi \\ &= 144 \pi - 25 \pi \\ &= 119 \pi \\ &\approx 373.85\,in^2 \\ \end{aligned}