Respuesta :

The area of shaded region is determined by difference of area of circle and area of sector.

First determine the area of circle is

[tex]A=\Pi\times r^2^{}[/tex]

The radius of circle is given as,

[tex]r=11.1\text{ m.}[/tex]

Substitute the value of radius in area of circle,

[tex]A_1=\text{ 3.14}\times(11.1)^2[/tex][tex]A_1=386.88m^2[/tex]

Similarly find the area of sector,

[tex]A_2=\frac{\theta}{360^{\circ}}\times\Pi\times r^2[/tex]

The angle given is,

[tex]\theta=130^{\circ}[/tex]

Substitute the value,

[tex]A_2=\frac{130^{\circ}}{360^{\circ^{}}}\times3.14\times11.1^2[/tex][tex]A_2=0.3611\times386.88[/tex][tex]A_2=139.706m^2[/tex]

The shaded area is determined as,

[tex]A=A_1-A_2[/tex][tex]A=386.88-139.706[/tex]

Thus the area of shaded region is determined as,

[tex]A=247.173m^2[/tex]

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