Answer:
209.55in²
Step-by-step explanation:
Find area of sector CADE
Radius =22 in
Angle=90°
Formula to apply is ;
Ф/360 × π × r² where
Ф=angle of sector, π=3.142 and r =radius of circle
[tex]A=\frac{90}{360} *3.142*22*22=380.182in^2[/tex]
Find area of triangle CAD where base length is 22 inches and height is 22 inches
Area of triangle formula is;
1/2×b×h where b is base and h is height
[tex]A=\frac{1}{2} *22*22=242in^2[/tex]
Find area remaining
380.182-242=138.182in²
Find the area of sector CBDF
Radius=28in
Angle=60°
Formula to apply is ;
Ф/360 × π × r² where
Ф=angle of sector, π=3.142 and r =radius of circle
[tex]A=\frac{60}{360} *3.142*28*28=410.55in^2[/tex]
Area of triangle BDC
The formula to apply is
1/2×a×a×sinФ where a=28 inches and Ф=60°
[tex]\frac{1}{2} *28*28*sin60=339.48in^2[/tex]
Remaining area
410.55-339.48=71.075in²
Area created by overlapping circles
138.182+71.075=209.26in²
