Fewpal
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How many parallelograms are there in the figure below?

(A) 14 

(B) 15

(C) 16 

(D) 18

2 Answers

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Best answer

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

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Answer:(D) 18

 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 .

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