Question

Alternate vertices of a regular hexagons are joined to form another regular hexagon

Answer 1

The 6 triangles of the star shaped figure formed are all equilateral, and the side of any one of these triangles is equal to the side of the inner hexagon. Also, start with drawing a perpendicular from one of the vertices of the inner hexagon to the nearest side of the outer hexagon; then use trigo (most of the angles involved are known).