Answer:
The area of shaded region is 226.4 meter squared.
Step-by-step explanation:
Radius of the circle = r =18.6 m
Angle subtended by chord[tex]\theta = 123^o[/tex]
Area of sector = [tex]\frac{\theta }{360^o}\pi r^2[/tex]
In ΔOAB
∠A+∠B+∠O= 180°
2∠A+123°= 180°(∠A=∠B, isosceles triangle)
∠A=∠B=28.5°
AC=BC (Radius of the circle bisects the chord at right angle.)...(1)
In ΔOAC
[tex]\sin 123^0=\frac{OC}{OA}[/tex]
OC = 8.87 m
[tex]\cos 123^0=\frac{AC}{OA}[/tex]
AC = 16.34 m
AB = AC+AB=16.34 m+16.34 m=32.68 m (from (1))
Area of the ΔOAB = [tex]\frac{1}{2}\times OC\times AB[/tex]
=[tex]\frac{1}{2}\times 8.87 m\times 32.68 m=144.93 m^2[/tex]
Area of segment = Area of sector - Area of triangle:
[tex]371.34 m^2-144.93 m^2=226.41 m^2\approx 226.4 m^2[/tex]
The area of shaded region is 226.4 meter squared.
