question_answer

Find the number of parallelograms contained in the following figure.

A)  34                         

B)         45

C)  42                                         

D)  47

Correct Answer: B

Solution :

The figure may be labelled as shown. The parallelogram composed of two components each are ADME, DFNM, EMOG, FHJN, MNKO, GOLl, HBJN, NJKO, OKLI, FHNM, MNOG, DFME, HJKN, NKLO, OLCI, FNOM, MOIG and DMGE. i.e. 18 in number. The parallelogram composed of four components each are  HOKB, NIU, FGOH, HOU, NICK, FGIN, FMJB, DENH, MGKJ,   B                 MGCL,DEIO, FMLK, AENF, AGOD, DMJH, DOKF, EILM and EGKN i.e. 18 in number.                 The parallelogram composed of eight components each are FGKB, FGCK and AGKF i.e. 3in number.                 \[\therefore \] Total number of parallelograms in the figure = 18 + 18 + 6 + 3 = 45