Calculate perimeter of a regular hexagon with vertices on a circle of diameter 1 centimetre.

The figure is shown below:

Diameter of circle, CF = 1 centimetre

∴ Radius of circle = cm = 0.5 cm

As can be seen from figure,

Radius of circle = Side of Hexagon

∴ Side of Hexagon = 0.5 cm

Perimeter of Hexagon = 6 × Side of Hexagon

= 6 × 0.5

= 3 cm