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

Answer: (c)

We may the label the figure as shown

The Simplest triangles are ADE,BDF, DEF and EFC i.e., 4 in number

There is only one triangle ABC composed of four components.

Thus, there are 4 + 1 = 5 triangles in the given figure.

Answer: (c)

We may the label the figure as shown

The Simplest triangles are ABG, BCG, CGE, CDE, AGE and AEF i.e., 6 in number.

The triangles composed of two components each are ABE, ABC, BCE and ACE i.e., 4 in number.

Thus, there are 6 + 4 = 10. triangles in the given figure.

Answer: (a)

There are a total of 19 squares in the figure, which have been marked as shown in the following figure.

There are three suqares in the upper row □EFIH, □FGJI, □GBLJ.

There are five suqares in the middle row namely □TQRS, □QHPR, □HIOP, □IJNO, □JLMN

There are three suqares in the lower row namely □SRUD, □RPVU, □POWV

By combining two upper rows there are three suqares namely □AEPS, □EGNP, □FBMO.

By combining two lower rows there are three suqares namely □ THVD, □ QIWU, □ ILCW

From all the three rows combined together there are two suqres namely □ AFWD and □ EBCV

∴Total number of squares = 3 + 5 + 3 + 3 + 3 + 2 = 19

Answer: (a)

The figure, in question has been labelled at different points as shown in the following figure

From the above diagram parallelograms are as follow

i) Parallelograms from the outer figure = ▱ABCD, ▱AIJD, ▱GBCH, ▱ADHG, ▱GHJI, ▱IJCB = 6

ii) Parallelograms from the upper half of the figure = ▱AGKE, ▱GILK, ▱IBFL, ▱AILE, ▱GBFK, ▱ABFE = 6

iii) Parallelograms from the lower half of the figure = ▱EKHD, ▱KLJH, ▱LFCJ, ▱KFCH, ▱ELJD, ▱EFCD = 6

∴ there are a total of 18 parallelograms in the figure.

Shortcut Method

Number of parallelograms = (3 + 2 + 1) × (2 + 1)

[∵ C = 3, R = 2]

= 6 × 3 = 18

Answer: (d)

The figure may be labelled as shown

The Simplest triangles are AHL, LHG, GHM, HMB, GMF, BMF, BIF, CIF, FNC, CNJ, FNE, NEJ, EKJ and JKD i.e.,14 in number.

The triangles composed of two components each are AGH, BHG, HBF, BFG, HFG, BCF, CJF, CJE, JEF, CFE and JED i.e.,11 in number.

The triangles composed of four components each are ABG, CBG, BCE and CED i.e.,4 in number.

∴ Total number of triangles in the given figure = 14 + 11 + 4 = 29.