Question

In the following question, count the number of triangles and squares in the given figure.

• A. $28$ triangles, $3$ squares
• B. $24$ triangles, $5$ squares
• C. $28$ triangles, $5$ squares
• D. $24$ triangles, $3$ squares

Answer 1

Answer: (C)

$28$ triangles, $5$ squares

Triangles:
The, simplest triangles are $ABI,BGI,GHI,HAI,BCJ,CFJ,FGJ,GBJ,CDK,DEK,EFK$ and $FCK$ i.e. $12$ in number. The triangles composed of two components each are $ABG,BGH,GHA,HAB,BCF,CFG,FGB,GBC,CDE,DEF,EFC$ and $FGD$ i.e. $12$ in number. The triangles composed of four components each are $AGC,BFD,HBF$ and $GCE$ i.e. $4$ in number. Thus, there are $12+12+4=28$ triangles in the given figure.
Squares:
The squares composed of two components each are $BJGI$ and $CKFJ$ i.e. $2$ in number. The squares composed of four components each are $ABGH,BCFG$ and $CDEF$ i.e. $3$ in number. Total number of squares in the figure $=2+3=5.$