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The problem shown involves calculating the perimeter of the shaded region in the figure, which is part of a sector of a circle.

### Given Information:
- The angle at \( \angle ABC = 120^\circ \).
- The length of \( AB = 14 \, \text{cm} \).

The shaded region's perimeter includes three parts:
1. The arc length of sector \( BC \),
2. The straight line \( AB \),
3. The straight line \( AC \).

### Step-by-Step Approach:

1. **Find the radius**:  
   Since \( AB \) is a straight line from the center of the circle to a point on the circle, it represents the radius, \( r = 14 \, \text{cm} \).

2. **Arc length \( BC \)**:  
   The formula for the length of an arc is given by:
   \[
   L_{arc} = \frac{\theta}{360^\circ} \times 2\pi r
   \]
   where \( \theta = 120^\circ \) and \( r = 14 \, \text{cm} \).
   \[
   L_{arc} = \frac{120^\circ}{360^\circ} \times 2 \times \pi \times 14 = \frac{1}{3} \times 2 \times \pi \times 14 = \frac{28\pi}{3}
   \]

3. **Perimeter of the shaded region**:  
   The total perimeter of the shaded region is the sum of the arc length \( BC \), the straight line \( AB \), and the straight line \( AC \). Since \( AB = AC = 14 \, \text{cm} \), we have:
   \[
   P = L_{arc} + AB + AC = \frac{28\pi}{3} + 14 + 14
   \]
   \[
   P = \frac{28\pi}{3} + 28
   \]

4. **Approximate the result**:  
   Using \( \pi \approx 3.14 \):
   \[
   P = \frac{28 \times 3.14}{3} + 28 = \frac{87.92}{3} + 28 \approx 29.31 + 28 = 57.31 \, \text{cm}
   \]

Thus, the correct answer would be **approximately** \( \frac{190}{3} \), which corresponds to **Option A**.

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Do you need further clarification or details?

Here are some related questions to explore:
1. How do you find the area of a sector?
2. What is the formula for the circumference of a circle?
3. What are the steps to calculate the total angle of a sector?
4. How does changing the angle \( \theta \) affect the arc length?
5. How would the result change if the radius was doubled?

**Tip**: Always ensure units are consistent when working with circle formulas.

Given a sector of a circle with angle ABC = 120°, and AB = 14 cm, what is the perimeter of the shaded region?

Learn how to calculate the perimeter of a sector of a circle with a 120° angle and radius 14 cm. This problem involves key geometry concepts such as arc length and perimeter calculations. Suitable for Grades 9-11.

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