Question

How many parallelograms are there in the figure given below?

• A. $11$
• B. $14$
• C. $17$
• D. $15$

Answer 1

The correct option is D $15$


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, ABHJ 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 $=2+2+8+3=15.$