counting figures model question set 3 Practice Questions Answers Test with Solutions & More Shortcuts

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

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: (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: (d)

The figure, in question may be labelled as shown in following figure.

There are 12 triangles in the figure, namely ΔEOG, ΔAGK, ΔKOR, ΔKGT, ΔTUP, ΔRUS, ΔSPV, ΔSUW, ΔWNQ, ΔVNH, ΔHQJ and ΔHNC.

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