In each of the the following question, count the number of triangles and squares in the given figure.
After labelling the figure, we get the following, Simplest triangles IJQ, JKQ, KLQ, LMQ, MNQ, NOQ, OPQ, and PIQ (8)
- Triangles with two components each ABQ, BCQ, CDQ, DEQ, EFQ, FGQ, GHQ, HAQ, IKQ, KMQ, MOQ, and OIQ (12)
- Triangles with four components each ACQ, CEQ, EGQ, GAQ, IKM, KMO, MOI and OIK (8)
- Triangles with eight components each ACE, CEG, EGA and GAC (4)
Total number of triangles in the figure is 8 + 12 + 8 + 4 = 32
Also we need to count the number of squares in this figure,
- Squares with two components each IJQP, JKLQ, QLMN, and PQNO (4)
- Squares with four components each ABQH, BCDQ, QDEF and HQFG (4)
- Square with eight components is IKMO (1)
- Square with sixteen components is ACEG (1)
Total number of squares in the figure is 4 + 4 + 1 + 1 = 10
Hence option C is correct.