English and Logical Reasoning Prep GuideLogical ReasoningCounting of Figures
Count the number of triangles and squares in the given figure.
Options
- A28 triangles, 10 squares
- B28 triangles, 8 squares
- C32 triangles, 10 squares
- D32 triangles, 8 squares
Correct answer
C. 32 triangles, 10 squares
Step-by-step solution
We may label the figure as shown. 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 triangle 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