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

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: (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)

9 Quadrilaterals are as follow

□AGDH, □BAFD, □CAED, □AGDF, □AGDE, □ABDH, □ACDH, □ACDF and □ABDE

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