MCQ Test: Images and Figure Counting - 1 - Bank Exams MCQ

We may label the figure as shown.

• 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 triangle 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 the 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.

Hence, option C is correct.

The figure may be labelled as shown.

• The squares composed of two components each are BJMI, CKMJ , DLMK and AIML i.e. 4 in number.
• The squares composed of three components each are EBMA, BFCM, MCGD and AMDH i.e. 4 in number.
• The squares composed of four components each are VWBA, XYCB, ZA1DC and B1C1AD i.e. 4 in number.
• The squares composed of seven components each are NOJL, PQKI, RSLJ and TULK i.e. 4 in number.
• There is only one square i.e. ABCD composed of eight components.
• There is only one square i.e. EFGH composed of twelve components.

∴ Total number of squares in the figure = 4 + 4 + 4 + 4 + 1 + 1 = 18.

Hence, option C is correct.

The figure may be lebelled as shown.

• The simplest triangles are AHL, LHG, GHM, HMB, GMF, BMF, BIF, CIF, FNC, CNJ, FNE, NEJ, EKJ and JKD i.e. 14 in number.
• The triangles composed of two components each are AGH, BHG, HBF, BFG, HFG, BCF, CJF, CJE, JEF, CFE and JED i.e. 11 in number.
• The triangles composed of four components each are ABG, CBG, BCE and CED i.e. 4 in number.

∴ Total number of triangles in the given figure = 14 + 11 + 4 = 29.

Hence, option C is correct.

We may label the figure as shown.

• 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 CLG i.e. 6 in number. 

∴  Total number of trianngles in the figure = 8 + 10 + 6 = 24. 

Hence, option B is correct.

The figure may be labelled as shown.

• The simplest triangles are ABG, BCG, CGE, CDE, AGE and AEF i.e. 6 in number. 
• The triangles composed of three components each are ABE, ABC, BCE and ACE i.e. 4 in number.

∴ There are 6 + 4 = 10 triangles in the figure. 

Hence, option B is correct.

The figure may be labelled as shown.

• The simplest triangles are GLK, DLJ, DJM, HMN, QRE, IRA, IPA and FPO i.e. 8 in number. 
• The triangle having two components each are BDO, CDQ, DLM, PRA, KFI, NEI, HJI, GJI, DKI and DNI i.e. 10 in number.
• The triangles having four components each are DIE, DFI, DOA, DQA and GHI i.e. 5 in number.
• The triangles having six components each are DCA and DBA i.e. 2 in number.
• DEF is the only triangle having eight components.
• ABC is the only triangle having twelve components.

Thus, there are 8 + 10 + 5 + 2 + 1 + 1 =27 triangles in the figure. 

Hence, option A is correct.

We may label the figure as shown.

• The simplest triangles are AGH, GFO, LFO, DJK, EKP, PEL and IMN i.e. 7 in number.
• The triangles having two components each are GFL, KEL, AMO, NDP, BHN, CMJ, NEJ and HFM i.e. 8 in number.
• The triangles having three components each are IOE, IFP, BIF and CEI i.e. 4 in number.
• The triangles having four components each are ANE and DMF i.e. 2 in number. 
• The triangles having five components each are FCK, BGE and ADL i.e. 3 in number. 
• The triangles having Six components each are BPF, COE, DHF and AJE i.e. 4 in number. 

Thus, there are 7 + 8 + 4 + 2 + 3 + 4 = 28 triangles in the figure. 

We may lebel the figure as shown.

• The simplest triangles are BFG, CGH, EFM, FMG, GMN, GHN, HNI, LMK, MNK and KNJ i.e. 10 in number.
• The triangles composed of three components each are FAK and HKD i.e. 2 in number.
• The triangles composed of four components each are BEN, CMI, GLJ and FHK i.e. 4 in number.
• The triangles composed of eight components each are BAJ and CLD i.e. 2 in number.
• Thus, there are 10 + 2 + 4 + 2 = 18 triangles in the given figure.

Hence, option C is correct.

The figure may be labelled as shown.

• The simplest triangles are ABF, BFG, BCG, CGH, GHD, GED, EFG and AFE i.e. 8 in number.
• The triangles composed of two components each are ABG, BGE, AGE, ABE and GCD i.e. 5 in number.
• The triangles composed of three components each are BCD, CDE, BED, and BCE i.e. 4 in number.
• Thus, there are 8 + 5 + 4 = 17 triangles in the figure.

Hence, option C is correct.

The figure may be lebelled as shown.

The simplest triangles are AJF, FBG, GCH, HDI, and IEJ
i.e. 5 in number.
The triangles composed of three components each EBH, AIC, EFC, ADG, and BJD i.e. 5 in number.
Thus, there are 5 + 5 = 10 triangles in the figure.
Hence, option D is correct.

The total squares is in the give figure is 1²+2²+3²+4²=30

in the figure the 8 triangle is shown easily and another is COD , DOB, BOA, AOC, ACD, BDC,ABC, ABD so that total no. of triangle is 8+8=16

The figure shown the no. of triangle is in the diagram so that total no. of triangle is 8+8+8+4=28

The simplest triangle is shown in figure is 12 and another is IBO, BDO, DGO, GIO, ABO,CBD, DEO, IBD,BDG, DGI, GIB, ACO and COE and ACE is the total no of traingle are 12+14=26

In the figure the simplest Triangles are GLK, DLJ, DJM,HMN,QRE,IRA,IPA, and FPO is the 8 triangle

and another is BDO,CDQ,DLM, PRA, KFI, NEI, HJI, GJI,DKI, and DNI is the 10 triangle

and another is DIE, DFI, DOA, DQA, and GHI is the 5 triangle

and DCA, DBA is the 2 triangle and DEF and ABC so that according to the figure the total no. of triangle is 8+10+5+2+1+1=27