Counting of Parallelograms
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 grms are EMLA and NIDJ i.e. 2 in number. The
grms composed of two components each are BFMG, CGNH, GMKN, FGME, MNKL, FGNM, GHIN, and MNJK i.e. 9 in number . The
grms composed iof 3 components each are FGLA, ENKA, GHDJ and MIDK i.e. 4 in number. The
grms composed of 4 components each are FGJK, GHKL, FBNK, CHKM, EFHN and MFHI i.e. 6 in number . The
grms composed of 7 components each are FHKA and FHDK i.e. 2 in number.
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 grms are ABFE, BCGF, CDHG, EFJI, FGKJ and GHLK. There are 6 number . The
grms composed of two components each are ACGE, BDHF, EGKI, ABJI, BCKJ, and CDLK . Thus , there are 7 such
grms . The
grms composed of 3 components each are ADHE and AHLI i.e. 2 in number . The
grms composed of 4 components each are ACKI and BDLJ i.e. 2 in number. There is only 1
gm composed of six components ,namely ADLI . Thus , there are 6+7+2+2+1 = 18 parallelograms in the figures .
In the following figure, count the number of parallelograms.
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| Right Option : B | |||
| View Explanation | |||
In the following figure, count the number of parallelograms.
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| Right Option : A | |||
| View Explanation | |||
Find out the number of triangles in this figure.
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| Right Option : D | |||
| View Explanation | |||
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