Counting of Parallelograms


 
 
Concept Explanation
 

Counting of Parallelograms

Counting of Parallelograms :

In the counting of figures, you have a shape or a figure. From the given shape you will have to identify a given known shape and count the number of times it is present in the given shape. In thse types of questions, you have to count parallelograms in the given figure. Let us try some examples.

Example : In the following figuren, count the number of parallelograms.

A. 23

B 22

C. 21

D. 18

Answer : A

Explanation : The figure may be labelled as shown.

The simplest parallel grms are EMLA and NIDJ i.e. 2 in number. The parallel grms composed of two components each are BFMG, CGNH, GMKN, FGME, MNKL, FGNM, GHIN, and MNJK i.e. 9 in number . The parallel grms composed iof 3 components each are FGLA, ENKA, GHDJ and MIDK i.e. 4 in number. The parallel grms composed of 4 components each are FGJK, GHKL, FBNK, CHKM, EFHN and MFHI i.e. 6 in number . The parallel grms composed of 7 components each are FHKA and FHDK i.e. 2 in number. 

therefore Total number of parallelograms in the figure = 2+9+4+6+2 = 23

Example : In the following figure, count the number of parallelograms.

A. 20

B. 18

C. 16

D. 12

Answer : B

Explanation : The figure may be labelled as shown .

                   

The simplest parallel grms are ABFE, BCGF, CDHG, EFJI, FGKJ and GHLK. There are 6 number . The parallel grms composed of two components each are ACGE, BDHF, EGKI, ABJI, BCKJ, and CDLK . Thus , there are 7 such parallel grms . The parallel grms composed of 3 components each are ADHE and AHLI i.e. 2 in number . The parallel grms composed of 4 components each are ACKI and BDLJ i.e. 2 in number. There is only 1 parallel gm composed of six components ,namely ADLI . Thus , there are 6+7+2+2+1 = 18 parallelograms in the figures .

Sample Questions
(More Questions for each concept available in Login)
Question : 1

In the following figure, count the number of parallelograms.

Right Option : B
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Explanation
Question : 2

In each of the following questions , count the number of parallelograms in the given figures .

Right Option : D
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Explanation
Question : 3

In the following figure, count the number of parallelograms.

Right Option : A
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Explanation
 
 


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