We have that the formula for the area of the sector of a circle is:
[tex]A=\frac{\pi\cdot r^2\cdot\alpha}{360}[/tex]In this case, we have to find the area of the sector of a circle with radius r= 21 and then the area in the case of the r=21-14=7, and then find the difference.
Given the information, we have the following:
[tex]\begin{gathered} \alpha=130 \\ r_1=21 \\ r_2=7 \\ \Rightarrow A_1=\frac{(3.1416)(21)^2(130)}{360}=500.3 \\ \Rightarrow A_2=\frac{(3.1416)(7)^2(130)}{360}=55.6_{} \\ \Rightarrow A=A_1-A_2=500.3-55.6=444.7_{} \\ A=444.7 \end{gathered}[/tex]