First, we need to calculate the area of the complete circle
[tex]A=\pi\cdot r^2[/tex][tex]A=3.14\cdot9^2=254.34in^2\text{ }[/tex]
then we need to know the portion of the circle that is shaded
360°---- 100%
75° ------ x
[tex]x=\frac{75\cdot100}{360}=20.8\text{ \%}[/tex]
we need to obtain the 20.8 % of the area
254.34*(.208)=52.90in^2
the area shaded is 52.9 in^2
