counting figures model question set 1 Detailed Explanation And More Example

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: (a)

Smallest Triangles = ΔBOC, ΔCOD, ΔFOG, ΔGOH, ΔHOA, ΔAOB = 6

Triangles formed with two small triangles = ΔAOG, ΔAOC = 2

Largest Triangles = ΔACG, ΔEGC = 2

∴ Total Triangles = 6 + 2 + 2 = 10

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)