Question

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)

Answer 1

The length of the circumference is (being $d$ the diameter, and using 3.14 for $\pi$):

$L = 2 \cdot r \cdot \pi = d \cdot \pi = 4 \cdot \pi \text{ cm} = 12.56 \text{ cm}$

The perimeter of the hexagon is 12 cm.

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