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To solve the problem of finding the area of the sector, we will use the formula for the area of a sector of a circle. 

The formula for the area of a sector is:

\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]

Where:
- \(\theta\) is the central angle in degrees (here, \(270^\circ\)),
- \(r\) is the radius of the circle (the outer radius is 4 meters),
- \(\pi\) is given as \(3.14\).

### Steps to find the area of the sector:

1. **Outer circle area**:
   The radius of the outer circle is \(4\) meters. So, the area of the full outer circle is:
   \[
   A_{\text{outer}} = \pi r^2 = 3.14 \times 4^2 = 3.14 \times 16 = 50.24 \text{ square meters}
   \]

2. **Area of the full sector** (270°):
   Now, we find the area of the sector corresponding to a \(270^\circ\) angle:
   \[
   A_{\text{sector}} = \frac{270^\circ}{360^\circ} \times 50.24 = 0.75 \times 50.24 = 37.68 \text{ square meters}
   \]

Thus, the area of the sector is **37.7 square meters**, rounded to the nearest tenth.

If you have more specific instructions or details on the evaluation rubric, feel free to provide them!

Would you like more details or have any questions? Here are some related questions you could explore:

1. How would the area change if the central angle was 180° instead of 270°?
2. What would be the area if the radius was doubled to 8 meters?
3. How is the formula for the area of a sector derived from the area of a full circle?
4. What is the difference between the area of a sector and the area of a segment?
5. How do you find the circumference of the sector's arc for this problem?

**Tip**: Always remember to check if the units for the radius and the angle are correct before applying the formulas!

Find the area of a sector with a radius of 4 meters and a central angle of 270°. Use 3.14 for the value of π. Round your answer to the nearest tenth.

Learn how to find the area of a circle sector with a radius of 4 meters and a 270° central angle. Using 3.14 for π, this step-by-step solution demonstrates the formula for sector area and rounds to the nearest tenth. Ideal for high school geometry students.

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