Respuesta :
Given
The circumference of a circle is 7π
We need to find the area.
First of all, let's use the formula for the circumference of a circle and find the radius. Shown below:
[tex]\begin{gathered} \text{Circumference}=2\pi r \\ C=2\pi r \\ 7\pi=2\pi r \\ r=\frac{7\pi}{2\pi} \\ r=\frac{7}{2} \end{gathered}[/tex]Now, we can easily find the area by using this radius value in the formula for the area of a circle. Shown below:
[tex]\begin{gathered} \text{AreaofCircle}=\pi r^2 \\ A=\pi r^2 \\ A=\pi(\frac{7}{2})^2 \\ A=\pi(\frac{49}{4}) \\ A=\frac{49\pi}{4} \end{gathered}[/tex]Thus, the exact area of the circle is:
[tex]\frac{49\pi}{4}[/tex]