Area of regular polygon: regular hexagon and regular pentagon

Let X,Y,Z be respectively the areas of regular pentagon, regular hexagon and regular heptagon which are inscribed in a circle of radius 1. Then

Symmetry of a regular pentagon.

Area of a regular hexagon with side ‘a’ is

Lines of symmetry of a regular pentagon

The ratio of the measures of an interior angles of a regular hexagon to that of a regular dodecagon is: