To find the area of a sector of a circle, you can use the formula:
\[ \text{Area} = \frac{1}{2} r^2 \theta \]
where:
- \( r \) is the radius of the circle,
- \( \theta \) is the angle in radians.
In this case, you've provided:
- \( r = 3.5 \) cm,
- \( \theta = \frac{2\pi}{7} \) radians.
Now, substituting the values into the formula:
\[ \text{Area} = \frac{1}{2} \times (3.5)^2 \times \frac{2\pi}{7} \]
First, calculate \( (3.5)^2 \):
\[ (3.5)^2 = 12.25 \]
Now plug this back into the area formula:
\[ \text{Area} = \frac{1}{2} \times 12.25 \times \frac{2\pi}{7} \]
This simplifies to:
\[ \text{Area} = \frac{12.25 \times 2\pi}{14} = \frac{24.5\pi}{14} \]
Now simplify \( \frac{24.5\pi}{14} \):
\[ \text{Area} = \frac{24.5}{14} \pi = \frac{12.25}{7} \pi \approx 1.750 \pi , \text{cm}^2 \]
Finally, you can compute it numerically:
\[ \text{Area} \approx 1.750 \times 3.14159 \approx 5.50 , \text{cm}^2 \]
So, the area of the sector is approximately \( 5.50 , \text{cm}^2 \).