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Triangles : The simplest triangles are AEI, EOI, OHI, HAI, EBJ, BFJ, FOJ, OEJ, HOL, OGL, GDL, DHL, OFK, FCK, CGK and GOK i.e. 16 in number. The triangles composed of two components each are HAE, AEO, EOH, OHA, OEB, EBF, BFO, FOE, DHO, HOG, OGD, GDH, GOF, OFC, FCG and CGO i.e. 16 in number. The triangles composed of four components each are HEF, EFG, FGH, GHE, ABO, BGO, CDO and DAO i.e. 8 in...
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, RTKW and CVWM i.e. 4 in number. The rectangle composed of three components each are ACRP, PRMO, EGHT, THIK i.e. 4 in number. The rectangle composed of 4 components each are CEKM, AVSP, PSWO, VGHS and SHIW i.e. 5 in number. The rectangle composed of...
The simplest rectangles are ABJI, BCKJ, IJFG and JKEF i.e. 4 in number. The rectangle 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.
The horizontal lines are AE and JF i.e. 2 in number. The vertical lines are AJ, CH and EF i.e. 3 in number. The slanting lines are AG, BF, JD, IE, AB, DE, JI and FG i.e. 8 in number. Total number of straight lines needed to construct the figure =2+3+8=13
Simplest squares are EFRQ, MQYX, QRZY, RNSZ, LXWK, XYA1W, YZB1A1, ZSTB1, SGHT, WA1VP, A1B1UV, B1TOU and VUIJ i.e. 13 in number. The squares having two components each are AEYL, FBGZ, KA1JD, B1HCI i.e. 4 in number. The squares having four components each are MRB1W, QNTA, XZUP and YSOV i.e. 4 in number. The squares having seven components each are AFB1K, EBHA, LZID, and YGCJ i.e. 4 in...
The simplest triangles are IJO, BCJ, CDK, KQL, MLQ, GFM, GHN and NIO i.e. 8 in number. The triangles composed of two components each are ABO, AHO, NIJ, IGP, ICP, DEQ, FEQ, KLM, LCP and LGP i.e. 10 in number. The triangles composed of four components each are HAB, DEF, LGI, GIC, ICL and GLC i.e. 6 in number. Total triangles = 8 + 10 + 6 = 24
The simplest triangles are AHB, GHI, BJC, GFE, GIE, IJE, CEJ and CDE i.e. 8 in number. The triangles composed of two components each are HEG, BEC, HBE, JGE and ICE i.e. 5 in number. The triangles composed of three components each are FHE, GCE and BED i.e. 3 in number. There is only one triangle i.e. AGC composed of four components. There is only one triangle i.e. AFD composed of nine...
The simplest triangles are AGH, GFO, LFO, DJK, EKP, PEL and IMN i.e. 7 in number. The triangles composed of two components each are GFL, KEL, AMO, NDP, BHN, CMJ, NEJ and HFM i.e. 8 in number. The triangles composed of three components each are IOE, IFP, BIF and CEI i.e. 4 in number. The triangles composed of four components each are ANE, DMF i.e. 2 in number. The triangles composed of five...
Horizontal lines are IK, AB, HG and DC i.e. 4 in number. Vertical lines are AD, EH, JM, FG and BC i.e. 5 in number. Slanting lines are IE, JE, JF, KF, DE, DH, FC and GC i.e. 8 in number. So, total lines = 4 + 5 + 8 = 17
The simplest triangles are AHG, AIG, AIB, JFE, CJE, and CED i.e. 6 in number. The triangles composed of two components each are ABG, CFE, ACJ, EGI i.e. 4 in number. The triangles composed of three components each are ACE, AGE, CFD i.e. 3 in number. There is only one triangle AHE composed of four components. So, total = 6 + 4 + 3 + 1 = 14 
Vertically, in first column +1 increases and in second, +2 increases and in third, +3 increases. Hence answer is 9 lines.
Triangles: The simplest triangles are BGM, GHM, HAM, ABM, GIN, IJN, JHN, HGN, IKO, KLO, LJO, JIO, KDP, DEP, ELP, LKP, BCD and AFE i.e. 18 in number. The triangles composed of two components each are ABG, BGH, GHA, HAB, HGI, GIJ, IJH, JHG, JIK, IKL, KLJ, LJI, LKD, KDE, DEL, ELK i.e. 16 in number. The triangles composed of four components each are BHI, GJK, ILD, AGJ, HIL, JKE i.e. 6 in...
The space P, Q and R have to be shaded by three different colors definitely because these three spaces are adjacent to other two. Now, in order that no two adjacent spaces have same colour, the space T, U and S must be shaded with the color of P, Q and R respectively. Also the space X, V and W must be shaded with the color of the spaces S, T and U respectively i.e with the colors of the spaces...
The simplest squares are QUYX, URVY, YVSW and XYWT i.e. 4 in number. The square composed of two components each are IMYP, MJNY, YNKO, PYOL i.e. 4 in number. The square composed of three components each are AEYH, EBFY, YFCG, HYGD i.e. 4 in number. There is only one square i.e. QRST composed of four components. There is only one square i.e. IJKL composed of eight components. There is only one...
The quadrilaterals in the figure are ABCD, ABDE, ABDF, ABDH, CDHA, CDEA, CDFA, DEAG, DEFA, FAGD and AGDH. So, total number of quadrilaterals are 11.
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