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 = 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°

Hence,

ΔOAB is an equilateral triangle.

Area of ΔOAB = (Side)^{2}

= × (28)^{2}

= 196

= 333.2 cm^{2}

Area of sector OAPB = × r^{2}

= × × 28 × 28

= cm^{2}

Now,

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

= ( - 333.2) cm^{2}

Area of design = 6 × ( - 333.2)

= 2464 – 1999.2

= 464.8 cm^{2}

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

Cost of making 464.76 cm^{2} designs = 464.8 × 0.35

= Rs 162.68

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

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