counting figures model question set 2 Detailed Explanation And More Example

Answer: (c)

We shall join the centres of all the circles by horizontal and vertical lines and then label the resulting figure as shown.

The simplest squares are ABED, BCFE, DEHG, EFIH, GHKJ and HILK i.e., 6 in number.

The squares composed of four simple squares are ACIG and DFLJ i.e., 2 in number.

Thus, 6 + 2 = 8 squares will be formed.

Answer: (c)

Given figure can be labelled as follows

In the above figure, triangles formed by single units are ΔABE, ΔAEO, ΔAOF, ΔAFC, ΔDEB, ΔDOE, ΔDFO and ΔDCF i.e., 8 triangles.

Triangles formed by Combining 2 units are ΔABO, ΔAEF, ΔAOC, ΔBOD, ΔDEF, ΔDOC, ΔAED and ΔADF i.e., 8 triangles.

Triangles formed by Combining 3 units are ΔABF, ΔAEC, ΔBDF and ΔEDC i.e., 4 triangles.

Triangles formed by Combining 4 units are ΔABC, ΔBCD, ΔABD and ΔACD i.e., 4 triangles.

∴ Total number of Triangles = 8 + 8 + 4 + 4 = 24

Answer: (d)

We may the label the figure as shown

The Simplest triangles are AEI, AIH, BEJ, BJF, CFK, CKG, DGL, DLH, EOJ, FOJ, FOG, LOG, HOL and HOE i.e.,14 in number.

The triangles composed of two components each are EAH, FBE, BEO, EOF, BFO, FCG, GDH, HOD, HOG and GOD i.e.,10 in number.

The triangles composed of three components each are EFH, EHG, FGH and EFG i.e.,4 in number.

Thus, there are 14 + 10 + 4 = 28. triangles in the given figure.

Answer: (a)

The figure in question looks like as shown below after labelling it.

Smallest Triangles = ΔGAH, ΔHFL, ΔLCI, Δ IDJ ΔJBK, ΔKEG = 6

Largest Triangles = ΔABC, ΔEFD = 2

∴ Total Triangles = 6 + 2 = 8

Answer: (d)