The formula to find the area of a circle is:
[tex]\begin{gathered} A=\pi r^2 \\ \text{ Where A is the area and} \\ r\text{ is the radius of the circle} \end{gathered}[/tex][tex]\begin{gathered} \pi=3.14 \\ r=2\frac{1}{2}ft \end{gathered}[/tex]As the radius of the circle is a mixed fraction then we are going to convert it to an improper fraction and thus be able to work more easily with this number:
[tex]2\frac{1}{2}=\frac{2\cdot2+1}{2}=\frac{4+1}{2}=\frac{5}{2}[/tex]Now, you have:
[tex]\begin{gathered} r=2\frac{1}{2}ft \\ \text{ or} \\ r=\frac{5}{2}ft \end{gathered}[/tex]And then:
[tex]\begin{gathered} A=\pi r^2 \\ A=3.14\cdot(\frac{5}{2}ft)^2 \\ A=3.14\cdot(\frac{5}{2})^2ft^2 \\ A=3.14\cdot\frac{5^2}{2^2}^{}ft^2 \\ A=3.14\cdot\frac{25}{4}^{}ft^2 \\ A=\frac{3.14}{1}\cdot\frac{25}{4}^{}ft^2 \\ A=\frac{3.14\cdot25}{4}^{}ft^2 \\ A=\frac{78.5}{4}ft^2 \\ A=19.63ft^2 \end{gathered}[/tex]Therefore, the area of this circle will be 19.63 square feet.