Count the number of parallelogram in the given figure.

Solution

The figure may be labelled as shown. The simplest parallelograms are LMHJ and BDFM i.e. 2 in number. The parallelograms composed of two components each are ABML and MFGH i.e. 2 in number. The parallelograms composed of three components each are LBHI, LBEF, BDGH, DFLA, BCFH, KLFH, A6HJ and LFGJ i.e. 8 in number. The parallelograms composed of six components each are LCFI, KBEH and ADGJ i.e. 3 in number. Total number of parallelograms in the figure = 2 + 2 + 8 + 3 = 15.