The area of the sector of a circle whose radius 12 metres and whose angle at the centre is 42 is -----

Options

A. 26.4 sq. metres
B. 39.6 sq . Metres
C. 52.8 sq . Metres
D. 79.2 sq. metres

Answer

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

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

where:
- \(\theta\) is the angle at the center of the circle (in degrees),
- \(r\) is the radius of the circle.

### Step-by-Step Solution:

1. **Identify the given values:**
- Radius \(r = 12\) meters
- Angle \(\theta = 42\) degrees

2. **Substitute the values into the formula:**
\[ \text{Area of Sector} = \frac{42}{360} \times \pi \times (12)^2 \]

3. **Calculate \(12^2\):**
\[ 12^2 = 144 \]

4. **Substitute \(144\) back into the formula:**
\[ \text{Area of Sector} = \frac{42}{360} \times \pi \times 144 \]

5. **Simplify \(\frac{42}{360}\):**
\[ \frac{42}{360} = \frac{7}{60} \]

6. **Now substitute this back into the formula:**
\[ \text{Area of Sector} = \frac{7}{60} \times \pi \times 144 \]

7. **Calculate \(\frac{7 \times 144}{60}\):**
\[ 7 \times 144 = 1008 \]
\[ \frac{1008}{60} = 16.8 \]

8. **Now multiply by \(\pi\):**
\[ \text{Area of Sector} = 16.8 \pi \]

9. **Using \(\pi \approx 3.14\):**
\[ \text{Area of Sector} \approx 16.8 \times 3.14 \approx 52.792 \]

10. **Rounding to one decimal place:**
\[ \text{Area of Sector} \approx 52.8 \text{ square meters} \]

### Final Answer:
The area of the sector is approximately **52.8 square meters**.