A sector with a central angle measure of
\[\purpleD{200\degree}\] has a radius of
\[\maroonD{9\,\text{cm}}\].What is the area of the sector?

To find the area of a sector, we can use the formula:

\[
\text{Area of the sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]

Where:
- \(\theta\) is the central angle of the sector in degrees.
- \(r\) is the radius of the circle.

Given:
\[
\theta = 200^\circ, \quad r = 9\,\text{cm}
\]

Now, substitute the values into the formula:

\[
\text{Area of the sector} = \frac{200^\circ}{360^\circ} \times \pi \times (9\,\text{cm})^2
\]

First, simplify the fraction:

\[
\frac{200^\circ}{360^\circ} = \frac{5}{9}
\]

Now, calculate the area:

\[
\text{Area of the sector} = \frac{5}{9} \times \pi \times 81\,\text{cm}^2 = \frac{405\pi}{9}\,\text{cm}^2 = 45\pi\,\text{cm}^2
\]

So, the area of the sector is:

\[
\text{Area} \approx 45 \times 3.1416 \,\text{cm}^2 \approx 141.37\,\text{cm}^2
\]

Therefore, the area of the sector is approximately **141.37 square centimeters**.

Would you like more details or have any questions? 

Here are some related questions:
1. How do you find the perimeter of a sector?
2. What is the relationship between the area of a sector and the full circle?
3. How would the area change if the radius were doubled?
4. Can the formula for the area of a sector be applied to radians? How?
5. What is the significance of the central angle in determining the sector's area?

**Tip:** Always ensure the angle is in degrees (or convert to radians) when applying the sector area formula.

Learn how to calculate the area of a sector with a central angle of 200 degrees and a radius of 9 cm. This problem involves using the area of a sector formula and understanding circular sectors in geometry. Suitable for Grades 7-9 students.

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