# How many parallelograms are there in the figure below?

+1 vote
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How many parallelograms are there in the figure below? (A) 14

(B) 15

(C) 16

(D) 18

by (147k points)
selected

We can label the figure as shown. The simplest parallelograms are ABFE, BCGF, CDHG, EFJI, FGKJ and GHKL.

These are 6 in number.

The parallelograms composed of two components each, are ACGE, BDHF, EGKI, FHLJ, ABJI 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 parallelograms composed of six components, namely, ADLI.

Thus there are 6 + 7 + 2 +2 + 1 = 18 parallelograms in the figure.

Hence, total number of parallelograms are 18

by (51.1k points)

There are 6 parallelograms of one component
There are 7 parallelograms of two components
There are 2 parallelograms of three components
There are 2 parallelograms of four components
There is only one parallelograms of six components
∴ total number of parallelograms
=6+7+2+2+1=18 .