First, we need to calculate the area of the whole circle.
The area of a circle is computed as follows:
[tex]A=\pi r^2[/tex]The radius of circle F is EF = 14.
[tex]\begin{gathered} A=\pi\cdot14^2 \\ A=615.75 \end{gathered}[/tex]This area corresponds to 360°. To find the area that corresponds to 144°, we can use the next proportion:
[tex]\frac{615.75}{x}=\frac{360\text{ \degree}}{144\text{ \degree}}[/tex]Solving for x,
[tex]\begin{gathered} 615.75\cdot144=360\cdot x \\ \frac{615.75\cdot144}{360}=x \\ 246.3=x \end{gathered}[/tex]The area of sector EFG is 246.3
