Answer: 11.7 sq. m.
Step-by-step explanation:
The area of sector with angle x and radius r is given by :-
[tex]\text{Area of sector}=\frac{x}{360^{\circ}}\pi r^2[/tex]
Given: Diameter = 5.8 m
Then, radius =[tex]\frac{5.8}{2}=2.9\ m[/tex]
Now, the area of sector with angle 160° and radius 2.9 is given by :-
[tex]\text{Area of sector}=\frac{160^{\circ}}{360^{\circ}}\pi (2.9)^2\\\\\Rightarrow\ \text{Area of sector}=\frac{160{\circ}}{360^{\circ}}(3.14)(2.9)^2\\\\\Rightarrow\ \text{Area of sector}=11.7366222222\approx 11.7\ m^2[/tex]
