The circumference of a circle is give by:
[tex]C=2\pi r[/tex]Plugging the value we have for the circunference we can find the radius:
[tex]\begin{gathered} 31.4=2\pi r \\ r=\frac{31.4}{2\pi} \\ r=\frac{15.7}{\pi} \end{gathered}[/tex]Now that we have the radius we remember that the area of a circle is:
[tex]A=\pi r^2[/tex]Plugging the value of r we have that:
[tex]A=\pi(\frac{15.7}{\pi})^2=78.46[/tex]Therefore the area of the circle is 78.46
