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 when the degree measure of the angle at the center is \( \theta \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Area of a Circle**:
The area \( A \) of a circle with radius \( r \) is given by the formula:
\[ A = \pi r^2 \]

2. **Determine the Area for 360 Degrees**:
The area of the entire circle (which corresponds to an angle of 360 degrees) is:
\[ A_{360} = \pi r^2 \]

3. **Calculate the Area for 1 Degree**:
To find the area corresponding to 1 degree, we divide the total area by 360:
\[ A_{1} = \frac{\pi r^2}{360} \]

4. **Calculate the Area for \( \theta \) Degrees**:
Now, to find the area of the sector that corresponds to an angle of \( \theta \) degrees, we multiply the area of 1 degree by \( \theta \):
\[ A_{\theta} = \theta \times A_{1} = \theta \times \frac{\pi r^2}{360} \]

5. **Final Formula for the Area of the Sector**:
Therefore, the area of the sector with angle \( \theta \) is given by:
\[ A_{\theta} = \frac{\theta}{360} \times \pi r^2 \]

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