The circumference and the area of a circle are given by the formulas below
[tex]\begin{gathered} Circumference\rightarrow C=2\pi r \\ Area\rightarrow A=\pi r^2 \\ r\rightarrow radius \end{gathered}[/tex]Thus, in our case,
[tex]\begin{gathered} C=16\pi \\ \Rightarrow16\pi=2\pi r \\ \Rightarrow r=8 \end{gathered}[/tex]Finding the area,
[tex]\Rightarrow A=\pi *8^2=64\pi[/tex]