counting figures model question set 1 Detailed Explanation And More Example

Answer: (b)

The figure may be labelled as shown

Triangles

The Simplest triangles are KJN, KJO, CNB, OEF, JIL, JIM, BLA and MFG i.e.,8 in number.

The triangles composed of two components each are CDJ, EDJ, NKO, JLM, JAH and JGH i.e.,6 in number.

The triangles composed of three components each are BKI, FKI, CJA and EJG i.e.,4 in number.

The triangles composed of four components each are CDE and AJG i.e.,2 in number.

The only triangle composed of six components is BKF.

Thus, there are 8 + 6 + 4 + 2 + 1 = 21. triangles in the given figure.

Parallelograms:

The Simplest ||gms are NJLB and JOFM i.e.,2 in number.

The ||gms composed of two components each are CDKB, DEFK, BIHA and IFGH i.e.,4 in number.

The ||gms composed of three components each are BKJA, KFGJ, CJIB and JEFI i.e.,4 in number.

There is only one ||gm i.e., BFGA composed of four components.

The ||gms composed of five components each are CDJA, DEGJ, CJHA and JEGH i.e.,4 in number.

The only ||gm composed of six components is CEFB.

The only ||gm composed of ten components is CEGA.

Thus, there are 2 + 4 + 4 + 1+ 4 + 1 + 1 = 17. ||gms in the given figure.

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: (a)

The figure may be labelled as shown

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 and EGI i.e., 4 in number.

The triangles composed of three components each are ACE, AGE and CFD i.e., 3 in number.

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

Thus, there are 6 + 4 + 3 + 1 = 14 triangles in the given figure.

Answer: (a)

Answer: (c)

We may the label the figure as shown

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 and DMF i.e., 2 in number.

The triangles composed of five components each are FCK, BGE and ADL i.e., 3 in number.

The triangles composed of 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 given figure.