|A) 36 triangles, 7 Squares||B) 38 triangles, 9 Squares|
|C) 40 triangles, 7 Squares||D) 42 triangles, 9 Squares|
The figure may be labelled as shown
The Simplest triangles are BGM, GHM, HAM, ABM, GIN, IJN, JHN, HGN, IKO, KLO, LJO, JIO, KDP, DEP, ELP, LKP, BCD and AFE i.e 18 in number
The triangles composed of two components each are ABG, BGH, GHA, HAB, HGI, GIJ, IJH, JHG, JIK, IKL, KLJ,LJI, LKD, KDE, DEL and ELK i.e 16 in number.
The triangles composed of four components each are BHI, GJK, ILD, AGJ, HIL and JKE i.e 6 in number.
Total number of triangles in the figure = 18 + 16 + 6 =40.
The Squares composed of two components each are MGNH, NIOJ, and OKPL i.e 3 in number
The Squares composed of four components each are BGHA, GIJH, IKJL and KDEL i.e 4 in number
Total number of squares in the figure = 3 + 4 =7