S triangle AOB = S triangle BOCS = S triangle COD = S triangle DOE = S triangle EOF = S triangle FOA = S triangle AFN = S triangle BHC = S triangle MDE.

S triangle HMN = S triangle AOB+S triangle BOCS+S triangle COD+S triangle DOE+

S triangle EOF+S triangle FOA+S triangle AFN+S triangle BHC+

S triangle MDE

=9S triangle AOB

S regular hexagon = S triangle AOB+S triangle BOCS+S triangle COD+S triangle DOE+

S triangle EOF+S triangle FOA

= 6S triangle AOB

S triangle hmn: s regular hexagon = 9S triangle AOB :6S triangle AOB.

= 9:6

= 3:2