Given:
- Radius of the circle = 5.7 m
- Perimeter of the sector = 27.2 m

To Find:
- Area of the sector

Formula:
- Perimeter of the sector = Length of the arc + 2 * Radius
- Length of the arc = (Angle / 360) * 2 * π * Radius
- Area of the sector = (Angle / 360) * π * Radius^2

Solution:
1. Let's start by finding the length of the arc using the given information.
- Perimeter of the sector = Length of the arc + 2 * Radius
- 27.2 m = Length of the arc + 2 * 5.7 m
- Length of the arc = 27.2 m - 2 * 5.7 m
- Length of the arc = 27.2 m - 11.4 m
- Length of the arc = 15.8 m

2. Now, let's calculate the angle of the sector using the formula for the length of the arc.
- Length of the arc = (Angle / 360) * 2 * π * Radius
- 15.8 m = (Angle / 360) * 2 * 3.14 * 5.7 m
- 15.8 m = (Angle / 360) * 2 * 3.14 * 5.7 m
- 15.8 m = (Angle / 360) * 35.78 m
- Angle = (15.8 m * 360) / 35.78 m
- Angle ≈ 159.45 degrees

3. Finally, let's find the area of the sector using the angle of the sector.
- Area of the sector = (Angle / 360) * π * Radius^2
- Area of the sector = (159.45 / 360) * 3.14 * (5.7 m)^2
- Area of the sector = (0.44375) * 3.14 * 32.49 m^2
- Area of the sector ≈ 45.95 m^2

Answer:
The area of the sector is approximately 45.95 m^2.