Count the number of parallelogram in the given figure.

The figure may be labelled as shown.

The parallelograms composed of two components each are ADME, DFNM, EMOG, FHJN, MNKO, GOLI, HBJN, NJKO, OKLI, FHNM, MNOG, DFME, HJKN, NKLO, OLCI, FNOM, MOIG and DMGE. i.e. 18 in number.

The parallelograms composed of four components each are HOKB, NILJ, FGOH, HOLJ, NICK, FGIN, FMJB, DENH, MGKJ, MGCL, DEIO, FMLK, AENF, AGOD, DMJH, DOKF, EILM and EGKN i.e. 18 in number.

The parallelograms composed of six components each are AEJH, DAIL, DECL, DEJB, HILB and HICJ i.e. 6 in number.

The parallelograms composed of eight components each are FGKB, FGCK and AGKF i.e. 3 in number.

Total number of parallelograms in the figure = 18 + 18 + 6 + 3 = 45.