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 360o/6 = 60o at the centre of the circle.
∠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 cm2
Area of sector OAPB =
= 1/6 x 22/7 x 28 x 28
Area of segment APB = Area of sector OAPB − Area of ΔOAB
Therefore area of designs =
Cost of making 1 cm2 designs = Rs 0.35
Cost of making 464.76 cm2 designs = 464.8 x 0.35 =RS 162.68
Therefore, the cost of making such designs is Rs 162.68.