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To find the area of the shaded region (which is part of a sector of a circle), we first calculate the area of the entire sector using the given formula:

\[
\text{Sector Area} = \left( \frac{\text{angle of sector}}{360} \right) \pi r^2
\]

### Given values:
- Angle of the sector = \( 129^\circ \)
- Radius \( r \) = 8 cm

### Step-by-step calculation:
1. First, we plug the values into the formula:

\[
\text{Sector Area} = \left( \frac{129}{360} \right) \pi (8)^2
\]

2. Simplify the equation:

\[
\text{Sector Area} = \left( \frac{129}{360} \right) \pi \times 64
\]

\[
\text{Sector Area} = \left( 0.3583 \right) \pi \times 64
\]

3. Multiply the constants:

\[
\text{Sector Area} \approx 0.3583 \times 201.0619 \, \text{cm}^2
\]

4. The area of the sector is approximately:

\[
\text{Sector Area} \approx 72.0627 \, \text{cm}^2
\]

So, the area of the sector is \( 72.0627 \, \text{cm}^2 \), rounded to four decimal places.

Would you like further details or clarifications on this solution?

Here are five related questions for practice:
1. How would you calculate the area of a sector if the angle was halved?
2. What is the formula for calculating the circumference of the circle from the same problem?
3. How would the area change if the radius were doubled but the angle stayed the same?
4. What is the ratio of the area of the sector to the area of the whole circle?
5. How do you find the arc length of this sector?

**Tip:** Remember that sectors are just fractions of a circle. To calculate any sector's area or perimeter, you first find the full circle's values and then take the relevant fraction based on the angle.

Follow the steps to find the area of the shaded region using the formula for the area of a sector. Given an angle of 129° and a radius of 8 cm.

Learn how to calculate the area of a sector with a 129° angle and an 8 cm radius. Follow the step-by-step formula for determining the sector's area and round your result to four decimal places. Suitable for Grades 8-10.

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