Answer:
Area of the given figure is [tex]24.0[/tex] [tex]in^2[/tex]
Step-by-step explanation:
Area of sector of a circle with radius r and central angle [tex]\theta[/tex]
is given by
Area of sector = [tex]\frac{\theta}{360} \pi r^2[/tex]
here we have
[tex]r= 4[/tex] [tex]in[/tex]
[tex]\theta =172 degree[/tex]
Now we plug the values in the formula
so we have
Area of sector = [tex]\frac{172}{360} \pi (4)^2[/tex]
= [tex]\frac{172}{360} (3.14)(16)[/tex]
=[tex]24.0[/tex] [tex]in^2[/tex]
Hence the area of the given figure is [tex]24.0[/tex] [tex]in^2[/tex]
