counting figures model question set 1 Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (a)

The figure in question has been labelled as shown in the following figure

Smallest Triangles = ΔEAP, ΔEDP, ΔAGB, ΔHFG, ΔGBF, ΔPHD = 6

Triangles formed with two triangles = ΔEAD, ΔAGD, ΔBHF, ΔEHD, ΔAPF, ΔABF= 6

Largest Triangles = ΔBDC, ΔAEF, ΔABD = 3

∴ Total Triangles = 6 + 6 + 3 = 15

Answer: (a)

Total 28 triangles are as follow

Answer: (c)

There are total 27 triangles in the given figure.

From this figure it is clear that,

Triangles formed by single units = ΔABC, ΔBDE, ΔBCE, ΔCEF, ΔDGH, ΔDHE, ΔHEI, ΔEIF, ΔFIJ, ΔGKL, ΔGLH, ΔLHM, ΔHMI, ΔMIN, ΔINJ, Δ NJO i.e., 16 triangles.

Triangles formed by Combining 4 triangles are ΔADF, ΔBGI, ΔCHJ, ΔDKM, ΔLEN, ΔMFO and ΔDFM i.e., 7 triangles.

Triangles formed by Combining 9 triangles are ΔAGJ, ΔBKN and ΔCLO i.e., 3 triangles.

One Triangle ΔAKO formed by complete figure

∴ Total number of Triangles = 16 + 7 + 3 + 1

Answer: (c)

Smallest hexagons = MBCQPN, OCDSRP, TNPVIJ, UPRWHI = 4

Medium hexagons = KLBCPJ, JNCDRI, IPDEFH, GFDCPH, HRCBNI, IPBALJ, LBCRIJ, NCDFHI, MBDSRN, TNRWHJ = 10

Largest hexagons = LBDFHJ = 1

∴Total hexagons = 4 + 10 + 1 = 15

Answer: (c)

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

There are nine triangles in the upper half of the figure = ΔAEI, ΔAIG, ΔAEG, ΔGEO, ΔGBJ, ΔBFJ, ΔGBF, ΔGOF and ΔGEF.

Similarly, there are nine triangles in the lower half figure i.e., EFCD.

There are two more triangles ΔEGH and ΔFGH.

Hence, there are atotal of 20 triangles.