counting figures model question set 2 Detailed Explanation And More Example

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)

The figure may be labelled as shown

Triangles

The Simplest triangles are JBO, BKO, KDO, DFO, FGO, GHO, HIO, IJO, ABJ, BCK, CKD and DEF i.e.,12 in number.

The triangles composed of two components each are IBO, BDO, DGO, GIO, ABO, CBD and DEO i.e.,7 in number.

The triangles composed of four components each are IBD, BDG, DGI, GIB, ACO and COE i.e.,6 in number.

There is only one triangle ACE which is composed of eight components.

Thus, there are 12 + 7 + 6 + 1 = 26 triangles in the given figure.

Squares

The squares composed of two components each are BKOJ, KDFO, OFGH and JOHI i.e.,4 in number.

There is only one square i.e., CDOB composed of four components.

There is only one square i.e., BDGI composed of eight components.

Thus, there are 4 + 1 + 1 = 6 squares in the given figure.

Answer: (a)

The figure may be labelled as shown

The Simplest triangles are EFH, BIC, GHJ, GIJ, EKD and CKD i.e.,6 in number.

The triangles composed of two components each are ABJ, AFJ, GCK, GEK, CED and GHI i.e.,6 in number.

The triangles composed of three components each are GCD, GED, DJB and DJF i.e.,4 in number.

The triangles composed of four components each are ABF and GCE i.e.,2 in number.

The triangles composed of five components each are ABD and AFD i.e.,2 in number.

There is only one triangle i.e., FBD composed of six components.

Thus, there are 6 + 6 + 4 + 2 + 2 + 1 = 21 triangles in the given figure.

Answer: (a)

We shall label the figure as shown

The Simplest rectangles are ABJI, BCKJ, IJFG and JKEF i.e.,4 in number.

The rectangles composed of two components each are ACKI, BCEF, IKEG and ABFG i.e.,4 in number.

The only rectangle composed of four components is ACEG.

Thus, there are 4 +4 + 1 = 9. rectangles in the given figure.