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Questions  >>  Olympiad-Math  >>  Class 10
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Q)

Count the number of parallelogram in the given figure.

$ (A) 8 \\ (B) 11 \\(C)12 \\ (D)15 $

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A)
Solution :
The figure may be labelled as shown.
The simplest parallelograms are LMHJ and BDFM i.e. 2 in number. The parallelograms composed of two components each are ABML and MFGH i.e. 2 in number.
The parallelograms composed of three components each are LBHI, LBEF, BDGH, DFLA, BCFH, KLFH, A6HJ and LFGJ i.e. 8 in number.
The parallelograms composed of six components each are LCFI, KBEH and ADGJ i.e. 3 in number.
Total number of parallelograms in the figure = 2 + 2 + 8 + 3 = 15.
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