To find the area of a sector of a circle, you can use the formula:
\[ A = \frac{\theta}{360^\circ} \times \pi r^2 \]
where:
- \(A\) is the area of the sector,
- \(\theta\) is the angle in degrees,
- \(r\) is the radius of the circle.
Given:
- \(\theta = 115^\circ\)
- \(r = 6 , \text{cm}\)
Now we can substitute the values into the formula:
\[ A = \frac{115}{360} \times \pi \times (6)^2 \]
First, calculate \( (6)^2 \):
\[ (6)^2 = 36 \]
Now substitute this into the formula:
\[ A = \frac{115}{360} \times \pi \times 36 \]
Next, calculate \( \frac{115 \times 36}{360} \):
\[ \frac{115 \times 36}{360} = \frac{4140}{360} = 11.5 \]
Now substitute back into the area formula:
\[ A = 11.5 \pi \]
Using an approximate value for \(\pi \approx 3.14\) to find the numerical area:
\[ A \approx 11.5 \times 3.14 \approx 36.13 , \text{cm}^2 \]
Thus, the area of the sector is:
\[ \boxed{36.13 , \text{cm}^2} \]