Count the number of parallelogram in the given figure.
A.
20
B.
18
C.
16
D.
12
Correct answer is B
The figure may be labelled as shown.
The simplest ||gms are ABFE, BCGF, CDHG, EFJI, FGKJ and GHLK. These are 6 in number.
The parallelograms composed of two components each are ACGE, BDHF, EGKI, FHLJ, ABJI, BCKJ and CDLK. Thus, there are 7 such parallelograms.
The parallelograms composed of three components each are ADHE and EHLI i.e. 2 in number.
The parallelograms composed of four components each are ACKI and BDLJ i.e. 2 in number
There is only one parallelogram composed of six components, namely ADLI.
Thus, there are 6 + 7 + 2 + 2 + 1 = 18 parallelograms in the figure.