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

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: (c)

The figure may be labelled as shown

The rectangles composed of two components each are HIJE, EKLF, FMNG, GPQH, AEOH, EBFO, OFCG and HOGD i.e.,8 in number.

The rectangles composed of four components each are ABFH, BCGE, CDHF, DAEG and EFGH i.e.,5 in number.

The rectangles composed of six components each are IJFG, KLGH, MNHE and PQEF i.e.,4 in number.

The rectangles composed of eight components each are IJMN, KLPQ and ABCD i.e.,3 in number.

Thus, there are 8 + 5 + 4 + 3 = 20. rectangles in the given figure.

(Here note that the squares are also counted amongest rectangles)

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)