The problem states that the length of an arc is (1)/(5) of its circumference. This means that the sector enclosed by this arc represents (1)/(5) of the entire circle.

The problem states that the length of an arc is $\frac{1}{5}$ of its circumference. This means that the sector enclosed by this arc represents $\frac{1}{5}$ of the entire circle.
The ratio of the arc length to the circumference is equal to the ratio of the sector's angle to $360^\circ$.

$$\frac{\text{Arc Length}}{\text{Circumference}} = \frac{\text{Angle of Sector}}{360^\circ} = \frac{1}{5}$$

The ratio of the area of a sector to the area of the entire circle is the same as the ratio of the arc length to the circumference (or the ratio of the sector's angle to $360^\circ$).

$$\frac{\text{Area of Sector}}{\text{Area of Circle}} = \frac{\text{Arc Length}}{\text{Circumference}}$$

Given that the area of the circle is $346.5 \text{ cm}^2$ and the arc length is $\frac{1}{5}$ of the circumference, we can write:

$$\frac{\text{Area of Sector}}{346.5 \text{ cm}^2} = \frac{1}{5}$$

To find the area of the sector, multiply the area of the circle by $\frac{1}{5}$:

$$\text{Area of Sector} = \frac{1}{5} \times 346.5 \text{ cm}^2$$ $$\text{Area of Sector} = 69.3 \text{ cm}^2$$

The final answer is $\text{69.3 cm}^2$.