Q:

Find area of shaded region. Round to the nearest tenth need help ASAP

Accepted Solution

A:
Answer:The area of shaded region is 226.4 meter squared.Step-by-step explanation:Radius of the circle = r =18.6 mAngle 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 mAB = 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.