Find the number of Squares and Triangles in a figure type questions coming in CET Exam. In each of the following questions, a set of figures is given followed by a set of five alternatives (A), (B), (C) and (D) (E) is provided. It is required to select the alternative which represents the number of Triangles or squares fitted into each other.
Find the number of triangles and squares in the given figure.
A. 44 triangles, 10 squares
B. 14 triangles, 16 squares
C. 27 triangles, 6 squares
D. 36 triangles, 9 squares
D. 30 triangles, 12 squares
Solution
Triangles :
The simplest triangles are AEI, EOI, OHI, HAI, EBJ, BFJ, FOJ, OEJ, HOL, OGL, GDL, DHL, OFK, FCK, CGK and GOK i.e. 16 in number.
The triangles composed of two components each are HAE, AEO, EOH, OHA, OEB, EBF, BFO, FOE, DHO, HOG, OGD, GDH, GOF, OFC, FCG and CGO i.e. 16 in number.
The triangles composed of four components each are HEF, EFG, FGH, GHE, ABO, BGO, CDO and DAO i.e. 8 in number.
The triangles composed of eight components each are DAB, ABC, BCD and CDA i.e. 4 in number.
Total number of triangles in the figure = 16 + 16 + 8 + 4 = 44.
Squares :
The squares composed of two components are HIOL, IEJO, JFKO and KGLO i.e. 4 in number.
The squares composed of four components are AEOH, EBFO, OFGC and HOGD i.e.4 in number.
There is only one square EFGH which is composed of eight components.
There is only one square ABCD which is composed of sixteen components.
Total number of squares in the figure = 4 + 4 + 1 + 1 = 10.
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