Exams

perimeter of window = πr+2r 

= [(22/7) x (63/2) + 63] = 99+63 = 162 cm

The figure may be labelled as shown 

Triangles :

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.

Squares :

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

The number of ways of arranging n beads in a necklace is (n-1)!2=(8-1)!2=7!2 = 2520 

(since n = 8)