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Questions  >>  Olympiad-Math  >>  Class 10

Count the number of parallelogram in the given figure.

$ (A) 23 \\ (B) 22 \\(C)21 \\ (D) 18 $

1 Answer

Solution :
The figure may be labelled as shown.
The simplest parallelograms are EMLA and NIDJ i.e. 2 in number.
The parallelograms composed of two components each are BFMG, CGNH, GMKN, FGME, GHNM, MNKL, FGNM, GHIN and MNJK i.e. 9 in number.
The parallelograms composed of three components each are FGLA, ENKA, GHDJ and MIDK ie. 4 in number.
The parallelograms composed of four components each are FGJK, GHKL, FBNK, CHKM, EFHN and MFHI i.e. 6 in number.
The parallelograms composed of seven components each are FHKA and FHDK i.e. 2 in number.
Total number of parallelograms in the figure = 2 + 9 + 4 + 6 + 2 = 23.
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