Counting
Counting Rectangles
Q1) Count the number of rectangles in the given figure 1) 15 2) 16 3) 18 4) 20 Solution: The figure may be labelled as shown.  The rectangles composed of two components each are HIJE, EKJ,F, FMNG, GPQH, AEOH, EBFO, OFCG and HOGD i.e. 8 in number. The rectangles composed of four components each are ABFH, BCGE, CDHF, DAEG and EFGH i.e. 5 in number. The rectangles composed of six components each are IJFG, KLGH, MNHE and PQEF i.e. 4 in number. The rectangles composed of eight components each are IJMN, KLPQ and ABCD i.e. 3 in number. Thus, there are 8 + 5 + 4 + 3 = 20 rectangles in the given figure. (Here note that the squares are also counted amongst rectangles) Q2) Count the number of rectangles in the given figure  1) 7 2) 8 3) 9 4) 10 Solution: The figure may be labelled as shown.  The simplest rectangles are ABJI, BCKJ, IJFG and JKEF i.e. 4 in number. The rectangles composed of two components each are ACKI, BCEF, IKEG and ABFG i.e. 4 in number. The only rectangle composed of four components is ACEG. Thus, there are 4 + 4 + 1 = 9 rectangles in the given figure. Read More: Questions on Counting number of SquaresDownload: Practice Questions on Counting Geometrical FiguresQ3) Count the number of rectangles and hexagons in the given figure  1) 30, 5 2) 32, 3 3) 28, 5 4) 30, 3 Solution: The figure may be labelled as shown.  Rectangles: The simplest rectangles are CVSR, VETS, RSWM and STKW i.e. 4 in number. The rectangles composed of two components each are CETR, VEKW, RTKM and CVWM i.e. 4 in number. The rectangles composed of three components each are ACRP, PRMO, EGHT and THIK i.e. 4 in number. The rectangles composed of four components each are CEKM, AVSP,PSWO, VGHS and SHIW i.e. 5 in number. The rectangles composed of five components each are AETP, PTKO, CGHR and RHIM i.e. 4 in number. The rectangles composed of six components each are ACMO and EGIK i.e. 2 in number. The rectangles composed of eight components each are AGHP, PHIO, AVWO and VGIW i.e. 4 in number. The rectangles composed of ten components each are AEKO and CGIM i.e. 2 in number. AGIO is the only rectangle having sixteen components. Total number of rectangles in the given figure = 4 + 4 + 4 + 5 + 4 + 2 + 4 + 2 + 1 = 30. Hexagons: The hexagons in the given figure are CDEKLM, CEUKMQ, CFHJMQ, BEUKNP and BFHJNP. So, there are 5 hexagons in the given figure. Read More: Questions on Counting number of TrianglesRead More: Shortcuts for Geometrical PatternsQ4) Count the number of rectangles in the given figure 1) 8 2) 17 3) 18 4) 20 Solution: The figure may be labelled as shown.  The simplest rectangles are ABQP, PQNO, BCDN, NDEM, MEFL, LFJK, FGHR and RHIJ i.e. 8 in number. The rectangles composed of two components each are ABNO, BCEM, NDFL, MEJK and FGIJ i.e. 5 in number. The rectangles composed of three components each are ACDO, BCFL, NDJK and LGIK i.e. 4 in number. There is only one rectangle i.e. BCJK composed of four components. Total number of rectangles in the figure = 8 + 5 + 4 + 1 = 18. Read More: Questions on Counting number of Parallelograms |