It can be observed that these designs are segments of the circle.

Consider segment APB. Chord AB is a side of the hexagon. Each chord will substitute 360^{o}/6 = 60^{o} at the centre of the circle.

In ΔOAB,

∠OAB = ∠OBA (As OA = OB)

∠AOB = 60°

∠OAB + ∠OBA + ∠AOB = 180°

2∠OAB = 180° − 60° = 120°

∠OAB = 60°

Therefore, ΔOAB is an equilateral triangle.

Area of ΔOAB =

= √3/4 x (28)^{2}=196√3

=196 x 1.7=333.2 cm^{2}

Area of sector OAPB =

= 1/6 x 22/7 x 28 x 28

=1232/3 cm^{2}

^{Area of segment APB = Area of sector OAPB − Area of ΔOAB}

^{}

Therefore area of designs =

=(2464-1999.2)cm^{2}

= 464.8cm^{2}

Cost of making 1 cm^{2} designs = Rs 0.35

Cost of making 464.76 cm^{2} designs = 464.8 x 0.35 =RS 162.68

Therefore, the cost of making such designs is Rs 162.68.