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

Answer: (a)

The figure, in question may be labelled as shown in following figure.

There are a total of 27 rectangles in the figure, namely

and there is 1 more rectangle ▭ ABCD.

Hence there are a total of 27 rectangles.

Answer: (b)

The above figure has following six parallelograms

▱ ABDC,▱ ABFE, ▱ BCED, ▱ BCGF, ▱ CDFE and ▱ DEGF.

Answer: (c)

Answer: (a)

Smallest and single rectangles

= ▭ABFE, ▭EFIH, ▭BCGF, ▭FGJI = 4

Rectangles formed with two rectangles

= ▭ABIH, ▭AEGC, ▭EGJH, ▭BCJI = 4

Largest rectangle = ▭ACJH = 1

∴ Total number of Rectangles = 4 + 4 + 1 = 9

Answer: (a)

We shall label the figure as shown

The Simplest triangles are AFJ, FJK, FKB, BKG, JKG, JGC, HJC, HIJ, DIH, DEI, EIJ and AEJ i.e., 12 in number.

The triangles composed of two components each are JFB, FBG, BJG, JFG, DEJ, EJH, DJH and DEH i.e., 8 in number.

The triangles composed of three components each are AJB, JBC, DJC and ADJ i.e., 4 in number.

The triangles composed of six components each are DAB, ABC, BCD and ADC i.e., 4 in number.

Thus, there are 12 + 8 + 4 + 4 = 28 triangles in the given figure.