Answer:
20.25π square feet
Explanation:
The circumference of a circle = 9π ft.
Given any circle of radius, r, its circumference is calculated using the formula:
[tex]C=2\pi r[/tex]Equating the two:
[tex]\begin{gathered} 2\pi r=9\pi \\ \text{ Divide both sides by }2\pi \\ \frac{2\pi r}{2\pi}=\frac{9\pi}{2\pi} \\ r=4.5\;ft. \end{gathered}[/tex]Next, we find the area of the circle.
The area of a circle is calculated using the formula:
[tex]Area=\pi r^2[/tex]Substitute the value of the radius, r obtained earlier:
[tex]\begin{gathered} A=\pi\times\left(\frac{9}{2}\right)^2 \\ =\frac{81}{4}\pi \\ =20.25\pi\;square\text{ feet} \end{gathered}[/tex]The area of the circle is 20.25π square feet.
