Answer :


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

Let us take segment APB.


Chord AB is a side of the regular hexagon.


And,


Each chord will substitute = 60o 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°


Hence,


ΔOAB is an equilateral triangle.


Area of ΔOAB = (Side)2


=  × (28)2


= 196


= 333.2 cm2


Area of sector OAPB = × r2


= × × 28 × 28


= cm2


Now,


Area of segment APB = Area of sector OAPB - Area of ΔOAB


= ( - 333.2) cm2


Area of design = 6 × ( - 333.2)


= 2464 – 1999.2


= 464.8 cm2


Cost of making 1 cm2 designs = Rs 0.35


Cost of making 464.76 cm2 designs = 464.8 × 0.35


= Rs 162.68


Hence, the cost of making such designs would be Rs 162.68.

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