Count the number of triangles and squares in the given figure.
28 triangles, 10 squares
28 triangles, 8 squares
32 triangles, 10 squares
32 triangles, 8 squares
Correct answer is C
The figure may be labelled as shown.
Triangles :
The simplest triangles are IJQ, JKQ, KLQ, LMQ, MNQ, NOQ, OPQ and PIQ i.e. 8 in number. The triangles composed of two components each are ABQ, BCQ, CDQ, DEQ, EFQ, FGQ, GHQ, HAQ, IKQ, KMQ, MOQ and OIQ i.e. 12 in number.
The triangles composed of four components each are ACQ, CEQ, EGQ, GAQ, IKM, KMO, MOI and OIK i.e. 8 in number.
The triangles composed of eight components each are ACE, CEG, EGA and GAC i.e. 4 in number.
Total number of triangles in the figure = 8 + 12 + 8 + 4 = 32.
Squares :
The squares composed of two components each are IJQP, JKLQ, QLMN and PQNO i.e. 4 in number.
The squares composed of four components each are ABQH, BCDQ, QDEF and HQFG i.e. 4 in number.
There is only one square i.e. IKMO composed of eight components.
There is only one square i.e. ACEG composed of sixteen components.
Thus, there are 4 + 4 + 1 + 1= 10 squares in the given figure.
