counting figures model question set 3 Detailed Explanation And More Example

Answer: (b)

The figure in question has been labelled as shown in the following figure

Smallest Triangles = ΔAEF, ΔEPR, ΔFSQ, ΔPRD, ΔRSD, ΔSQD = 6

Single Triangles = ΔPBD, ΔQDC, ΔEFD = 3

Triangles formed with two triangles = ΔPSD, ΔRQD, ΔFDQ, ΔEDP = 4

Triangles formed with three or four triangles = ΔAPQ, ΔFDC, ΔBDE, ΔPQD = 4

Largest Triangles = ΔABC = 1

∴ Total Triangles = 6 + 3 + 4 + 4 + 1 =18

Answer: (c)

We may the label the figure as shown

The Simplest triangles are ADE,BDF, DEF and EFC i.e., 4 in number

There is only one triangle ABC composed of four components.

Thus, there are 4 + 1 = 5 triangles in the given figure.

Answer: (c)

We may the label the figure as shown

The Simplest triangles are ABG, BCG, CGE, CDE, AGE and AEF i.e., 6 in number.

The triangles composed of two components each are ABE, ABC, BCE and ACE i.e., 4 in number.

Thus, there are 6 + 4 = 10. triangles in the given figure.

Answer: (d)

Pentagons in the figure as follow

Smallest pentagons = KLABM, BCDEN, EFGHO, HIJKP = 4

Medium pentagons = KMBEH, BNEHK, EOHKB, HPKBE = 4

Largest pentagons = KMBFG, BNEIJ, EOHLA, HPKCD = 4

∴Total pentagons = 4 + 4 + 4 = 12

Answer: (b)

In the given diagram, there are 22 triangles which can be better understood with the help of following diagram.

In the above figures,

Triangles consisting of 1 unit are ΔADG, ΔAGH, ΔAHE, ΔDMF, ΔFME, ΔDIB, ΔIBJ, ΔJBF, ΔCFL, ΔCLK and ΔCKE i.e., 11 triangles.

Triangles consisting of 2 units are ΔADH, ΔAGE, ΔDFE, ΔDBJ, ΔIBF, ΔECL and ΔCKF i.e., 7 triangles.

Triangles consisting of 3 units are ΔADE, ΔBDF and ΔCFE i.e., 3 triangles.

Triangles consisting of whole figure is ΔABC i.e., 1 triangle.

So, the total number of triangles = 11 + 7 + 3 + 1 = 22.

Answer: (c)

Horizontal lines = BL, CK, DJ, EI = 4

Slant lines = AE, LF, KG, AI, BH, CG, DF = 7

∴ Total number of straight lines = 4 + 7 = 11