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 \(\frac{360°}6\) = 60° 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 = \(\frac{\sqrt3 }4 \times (side)^2 \)
= \(\frac{\sqrt3}4 \times (28)^2\) =\(196 \sqrt3\) = \(196 \times 1.7 \)= 333.2 cm\(^2\)
Area of sector OAPB = \(\frac{60°}{ 360°} \times \pi r^2\)
= \(\frac{1}6 \times \frac{22}7 \times 28 \times 28\) = \(\frac{1232}3\) cm\(^2\)
Area of segment APB = Area of sector OAPB - Area of ΔOAB
∴ Area of designs = \(6 \times (\frac{1232}3 - 333.2) \)cm\(^2\)
= (2464 - 1999.2) cm\(^2\)
= 464.8 cm\(^2\)
Cost of making 1 cm\(^2\) designs = Rs 0.35
Cost of making 464.76 cm\(^2\) designs = \(464.8 \times 0.35\) = Rs 162.68
Therefore, the cost of making such designs is Rs 162.68.