Answer:
17π/2 square units
Step-by-step explanation:
The arc length is related to the angle and the radius by ...
s = rθ . . . . . r is the radius; θ is the central angle in radians, s is the length
The angle 20° is equivalent to (20°)×(π/180°) = π/9 radians. Then the radius can be found from ...
π/3 = r·π/9
3 = r . . . . . . . . . multiply by 9/π
The area of a sector is ...
A = 1/2r²θ
Here, the shaded sector has an angle measure in radians of 2π less the angle of the unshaded sector, π/9. That is, θ = 2 -π/9 = 17π/9. The area of the shading is ...
A = 1/2(3²)(17π/9) = 17π/2 . . . . square units
