counting figures model question set 3 Detailed Explanation And More Example

Answer: (a)

Horizontal lines = AC, LD, KE, JF, IG = 5

Vertical lines = AI, BH, CG =3

Slant lines = AG, IC = 2

∴ Total number of straight lines = 5 + 3 + 2 = 10

Answer: (b)

Smallest Triangles = ΔABC, ΔACD, ΔADE = 3

Triangles formed with two triangles = ΔABD, ΔACE, ΔADF = 3

Triangles formed with three triangles = ΔABE, ΔACF = 2

Largest Triangles = ΔAEF, ΔABF = 2

∴ Total Triangles = 3 + 3 + 2 + 2 = 10

Answer: (d)

The figure may be labelled as shown

The Simplest triangles are AGE, EGC, GFC, BGF, DGB and ADG i.e., 6 in number.

The triangles composed of two components each are AGC, BGC and ABG i.e., 3 in number.

The triangles composed of three components each are AFC, BEC, BDC, ABF, ABE and DAC i.e., 6 in number.

There is only one triangle i.e., ABC composed of six components.

Thus, there are 6 + 3 + 6 + 1 = 16 triangles in the given figure.

Answer: (a)

The figure may be labelled as shown

The Simplest triangles are ABL, BCD, DEF, FGP, PGH, QHI, JQI, KRJ and LRK i.e., 9 in number.

The triangles composed of two components each are OSG, SGQ, SPI, SRI, KSQ, KMS, FGH, JHI and JKL i.e., 9 in number.

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

The triangles composed of five components each are NEI, ANI, MCG and KCO i.e., 4 in number.

The triangles composed of six components each are GMK and KOG i.e., 2 in number.

There is only one triangle i.e., AEI composed of ten components.

There is only one triangle i.e., KCG composed of eleven components.

∴ Total number of triangles in the given figure.

9 + 9 + 1 + 4 +2 + 1 + 1 = 27.

Answer: (b)

From the figure, it is clear that there are 9 triangles in the upper half of the figure ABFE, namely ΔPEM, ΔPGI, ΔAEI, ΔEIN, ΔIKQ, ΔQOF, ΔIBF, ΔINF and ΔIEF.

Likewise, there are 9 triangles in the lower half EFCD of the main figure.

There are more triangles ΔEPR, ΔEIJ, ΔIFJ and ΔQFS.

Hence, there are a total of 22 triangles in the figure.

Answer: (d)

The figure may be labelled 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.