counting figures model question set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (c)

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 triangles 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 one triangle having eight components.

ABC is the only one triangle having twelve components.

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

Answer: (b)

The figure may be labelled as shown

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 and ELK i.e.,16 in number.

The triangles composed of four components each are BHI, GJK, ILD, AGJ, HIL and JKE i.e.,6 in number.

Thus, there are 18 + 16 + 6 = 40. triangles in the given figure.

Squares

The squares composed of two components each are MGNH, NIOJ and OKPL i.e.,3 in number.

The squares composed of four components each are BGHA, GIJH, IKLJ and KDEL i.e.,4 in number.

Thus, there are 3 + 4 = 7 squares in the given figure.

Answer: (d)

We may the label the figure as shown

The Simplest triangles are AFB, FEB, EBC, DEC, DFE and AFD i.e., 6 in number.

The triangles composed of two components each are AEB, FBC, DFC, ADE, DBE and ABD i.e., 6 in number.

The triangles composed of three components each are ADC and ABC i.e., 2 in number.

There is only one triangle i.e., DBC which is composed of four components.

Thus, there are 6 + 6 + 2 + 1 = 15 triangles in the given figure.

Answer: (b)

The figure may be labelled as shown

The Simplest triangles are ABJ, ACJ, BDH, DHF, CIE and GIE i.e.,6 in number.

The triangles composed of two components each are ABC, BDF, CEG, BHJ, JHK, JKI and CJI i.e.,7 in number.

There is only one triangle JHI which is composed of four components.

Thus, there are 6 + 7 + 1 = 14 triangles in the given figure.

Answer: (a)

The figure may be labelled 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.

Thus, there are 8 + 10 + 6 = 24. triangles in the given figure.