The circumference of a circle is give by:
![C=2\pi r](https://img.qammunity.org/2023/formulas/mathematics/high-school/noytl63lm1q06t23qsdkycir68uwxrmxzb.png)
Plugging the value we have for the circunference we can find the radius:
![\begin{gathered} 31.4=2\pi r \\ r=(31.4)/(2\pi) \\ r=(15.7)/(\pi) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/y5ujkg09bkuycxnvjkk240kv1hp7f85904.png)
Now that we have the radius we remember that the area of a circle is:
![A=\pi r^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/lcgfavc89jro4qntamn2b9gfliomu1jwuf.png)
Plugging the value of r we have that:
![A=\pi((15.7)/(\pi))^2=78.46](https://img.qammunity.org/2023/formulas/mathematics/college/inaminazdlfy4cq91eu4r20x7ou3pecug8.png)
Therefore the area of the circle is 78.46