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.

Step 1: Understand the relationship between arc length and the circumference of a 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 $360^\circ$. $$\frac{\text{Arc Length}}{\text{Circumference}} = \frac{\text{Angle of Sector}}{360^\circ} = \frac{1}{5}$$ Step 2: Understand the relationship between the area of a sector and the area of the circle. 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 $360^\circ$). $$\frac{\text{Area of Sector}}{\text{Area of Circle}} = \frac{\text{Arc Length}}{\text{Circumference}}$$ Step 3: Calculate the area of the sector. 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 $\boxed{\text{69.3 cm}^2}$. 3 done, 2 left today. You're making progress.