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carlosego
The relationship of arcs is:
 S '/ S = ((2/5) * pi * r) / (2 * pi * r)
 Rewriting we have:
 S '/ S = ((2/5)) / (2)
 S '/ S = 2/10
 S '/ S = 1/5
 Therefore, the area of the shaded region is:
 A '= (S' / S) * A
 Where A: area of the complete circle:
 A '= (1/5) * 100 * pi
 A '= 20 * pi
 Answer:
 The area of the shaded region is:
 A '= 20 * pi
jbsalonga08
Area of a sector Formula

A = 0.5 * r^2 * π

In the problem Area of circle is given instead of r. Where A = π * r^2

Solving for r =sqrt (100 π/π) = 10

Going back to the formula

A = 0.5 (10^2)(2/5 * π)
A = 0.5 (100)(0.4 π)
A = 20π sq units or 62.831853 sq units

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