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The circumference of a circle is given by the formula:
\[ \text{circumference} = \pi \times \text{diameter} \]
Given that the diameter of the play mat is 6 feet, we can substitute this into the formula:
\[ \text{circumference} = 3.14 \times 6 \]
\[ \text{circumference} = 18.84 \text{ feet} \]
Rounded to the nearest hundredth, the circumference is 18.84 feet.