Final answer:
The smallest possible perimeter of a regular hexagon with a side length correct to one decimal place and given as 6.8 cm is 40.5 cm. This is calculated by taking the lower bound of the side length, 6.75 cm, and multiplying it by the number of sides in a hexagon, which is 6.
Step-by-step explanation:
The perimeter of a regular hexagon can be found by multiplying the length of one side by the total number of sides, which is 6 for a hexagon. Since the length of a side is given as 6.8 cm correct to one decimal place, the smallest possible value for the length of a side would be 6.75 cm, as the next lower value rounded to one decimal place would be 6.8 cm.
Therefore, the smallest possible perimeter (P) of the hexagon would be:
P = 6 × side length = 6 × 6.75 cm = 40.5 cm