Question

PLZ HELP ASAP AREA OF A SECTOR

Answer 1

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

Answer 2

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