counting figures model question set 3 Detailed Explanation And More Example

Answer: (b)

There are five squares in the upper row of the main figure namely □AEQM, □EGRQ, □GISR, □IKTS, □KBNT.

Hence there are fifteen squares, five in each row of the main figure.

Similarly, there are total eight squares - Four in each bigger row formed by combining two rows at a time of the main figure. i.e., □AOVG, □EUWI, □GVXK, □IWPB, □MDHR, □QFJS, □RHLT, and □SJCN and finally there are three squares □AIJD, □EKLF and □GBCH from the main figure.

Hence, there are a total of 26 squares in the figure.

Shortcut Method:

Number of squares = (5 × 3) + (4 × 2) + (3 × 1) + (2 × 0)

= 15 + 8 + 3 + 0 = 26

Answer: (a)

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: (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: (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