counting figures model question set 2 Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

We may the label the figure as shown

The Simplest triangles are AEI, AIH, BEJ, BJF, CFK, CKG, DGL, DLH, EOJ, FOJ, FOG, LOG, HOL and HOE i.e.,14 in number.

The triangles composed of two components each are EAH, FBE, BEO, EOF, BFO, FCG, GDH, HOD, HOG and GOD i.e.,10 in number.

The triangles composed of three components each are EFH, EHG, FGH and EFG i.e.,4 in number.

Thus, there are 14 + 10 + 4 = 28. triangles in the given figure.

Answer: (d)

Naming the figure

Names of the squares are

Hence, there are 27 squares in this figure.

Answer: (d)

Horizontal lines = AB, EF, GH, CD, LM, PQ, ON = 7

Vertical lines = AC, EG, FH, BD, LO, MN = 6

∴ Total number of straight lines = 7 + 6 = 13

Answer: (a)

The figure may be labelled as shown

The horizontal lines are DF and BC i.e., 2 in number

The vertical lines are DG, AH and FI i.e., 3 in number

The slanting lines are AB, AC, BF and DC i.e., 4 in number

Thus, there are 2 + 3 + 4 = 9 straight lines in the figure.

Now, we shall count the number of triangles in the figure.

The Simplest triangles are ADE, AEF, DEK, EFK, DJK, FLK, DJB, FLC, BJG and LIC i.e.,10 in number.

The triangles composed of two components each are ADF, AFK, DFK, ADK, DKB, FCK, BKH, KHC, DGB and FIC i.e.,10 in number.

The triangles composed of three components each are DFJ and DFL i.e.,2 in number.

The triangles composed of four components each are ABK, ACK, BFI, CDG, DFB, DFC and BKC i.e.,7 in number.

The triangles composed of six components each are ABH, ACH, ABF, ACD, BFC and CDB i.e.,6 in number.

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

Thus, there are 10 + 10 + 2 + 7 + 6 +1 = 36 triangles in the given figure.

Answer: (c)

Smallest hexagons = KBCMHI, LCDNGH = 2

Largest hexagons = KBDNGI = 1

∴ Total hexagons = 2 + 1 = 3