The simplest ||gms are ABFE, BCGF, CDHG, EFJI, FGKJ and GHLK. These are 6 in number.
The parallelograms composed of two components each are ACGE, BDHF, EGKI, FHLJ, ABJI, BCKJ 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 parallelogram composed of six components, namely ADLI.
Thus, there are 6 + 7 + 2 + 2 + 1 = 18 parallelograms in the figure.
There is 6 columns with 2 cubes each.
Total boxes = 6 × 2 = 12
From first figure to second figure in the first unit of Question Figures the design rotates through 90° clockwise.
The simplest triangles are AFJ, FJK, FKB, BKG, JKG, JGC, HJC, HIJ, DIH, DEI, EIJ and AEJ i.e. 12 in number.
The triangles composed of two components each are JFB, FBG, BJG, JFG, DEJ, EJH, DJH and DEH i.e. 8 in number.
The triangles composed of three components each are AJB, JBC, DJC and ADJ i.e. 4 in number.
The triangles composed of six components each are DAB, ABC, BCD and ADC i.e. 4 in number.
Thus, there are 12 + 8 + 4 + 4 = 28 triangles in the figure.
From first figure to second figure the main design rotates through 45° anticlockwise and the arrow moves half step in anticlockwise direction.
The second figure is water image of the first figure.
NA
Triangles :
The simplest triangles are IJQ, JKQ, KLQ, LMQ, MNQ, NOQ, OPQ and PIQ i.e. 8 in number. The triangles composed of two components each are ABQ, BCQ, CDQ, DEQ, EFQ, FGQ, GHQ, HAQ, IKQ, KMQ, MOQ and OIQ i.e. 12 in number.
The triangles composed of four components each are ACQ, CEQ, EGQ, GAQ, IKM, KMO, MOI and OIK i.e. 8 in number.
The triangles composed of eight components each are ACE, CEG, EGA and GAC i.e. 4 in number.
Total number of triangles in the figure = 8 + 12 + 8 + 4 = 32.
Squares :
The squares composed of two components each are IJQP, JKLQ, QLMN and PQNO i.e. 4 in number.
The squares composed of four components each are ABQH, BCDQ, QDEF and HQFG i.e. 4 in number.
There is only one square i.e. IKMO composed of eight components.
There is only one square i.e. ACEG composed of sixteen components.
Thus, there are 4 + 4 + 1 + 1= 10 squares in the given figure.
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