A regular hexagon is drawn inside of a circle so that each of its vertices touches the circle. the diameter of the circle is 4 centimeters and the perimeter of the hexagon is 12 centimeters. how much longer is the circumference of the circle than the perimeter of the hexagon? (use 3.14 for pi)

The length of the circumference is (being [tex]d[/tex] the diameter, and using 3.14 for [tex]\pi[/tex]):

[tex]L = 2 \cdot r \cdot \pi = d \cdot \pi = 4 \cdot \pi \text{ cm} = 12.56 \text{ cm}[/tex]

The perimeter of the hexagon is 12 cm.

Hence, the circumference is 0.56 cm longer than the perimeter of the hexagon.