When degree measure of angle centre is `theta`, then what will be area of sector:

Options

A. `sqrt(3a)` cm
B. `theta/180^@xxpir`
C. `theta/360^@xxpir^2`
D. `theta/180^@xx2pir`

Answer

To find the area of a sector of a circle when the degree measure of the angle at the center is given as \( \theta \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Circle and Sector**:
- We have a circle with a center \( C \) and a radius \( r \).
- The angle at the center of the circle is \( \theta \) degrees.

2. **Area of the Circle**:
- The area \( A \) of the entire circle is given by the formula:
\[ A = \pi r^2 \]

3. **Proportion of the Circle**:
- The full circle corresponds to an angle of \( 360^\circ \).
- Therefore, the area of the circle that corresponds to \( 360^\circ \) is \( \pi r^2 \).

4. **Area per Degree**:
- To find the area covered by \( 1^\circ \), we can divide the total area by \( 360 \):
\[ \text{Area per degree} = \frac{\pi r^2}{360} \]

5. **Area of the Sector**:
- For an angle of \( \theta \) degrees, the area of the sector \( A_{\text{sector}} \) can be calculated by multiplying the area per degree by \( \theta \):
\[ A_{\text{sector}} = \theta \times \frac{\pi r^2}{360} \]

6. **Final Formula**:
- Thus, the area of the sector is given by:
\[ A_{\text{sector}} = \frac{\theta}{360} \times \pi r^2 \]

### Final Result:
The area of the sector when the degree measure of the angle at the center is \( \theta \) is:
\[ A_{\text{sector}} = \frac{\theta}{360} \pi r^2 \]