Respuesta :

jbsalonga08
The area of a sector is computed by below formula

Asector = 0.5*r^2*∅

where r is the radius and ∅ = angle measured in radians. 

In the picture r = 4 units and ∅ = 8/5(π)
Using the formula. 

A = 0.5 (4^2)(8/5*π)
A = (12.5)π or 40.122386 units
carlosego
The relationship of arcs is:
 S '/ S = ((8/5) * pi * 4) / (2 * pi * 4)
 Rewriting we have:
 S '/ S = ((8/5)) / (2)
 S '/ S = 8/10
 S '/ S = 4/5
 Therefore, the area of the shaded region is:
 A '= (S' / S) * A
 Where A: area of the complete circle:
 A '= (4/5) * pi * r ^ 2
 A '= (4/5) * pi * (4) ^ 2
 A '= (4/5) * pi * 16
 A '= (64/5) * pi
 Answer:
 The area of the shaded region is:
 A '= (64/5) * pi