Answer :

AB = 18 cm, DC = 32 cm

Distance between AB and DC = Height = 14 cm

Now, Area of the trapezium = (1/2) × (Sum of parallel sides) × Height

= (1/2) × (18+32) × 14 = 350cm^{2}

As AB ∥ DC, ∴ ∠ A +∠ D = 180°

and ∠ B +∠ C = 180°

Also, radius of each arc = 7 cm

Therefore,

Area of the sector with central angle A = (1/2) × (∠A/180) × π × r^{2}

Area of the sector with central angle D = (1/2) × (∠D/180) × π × r^{2}

Area of the sector with central angle B (1/2) × (∠B/180) × π × r^{2}

Area of the sector with central angle C = (1/2) × (∠C/180) × π × r^{2}

Total area of the sectors =

= 77 + 77 = 154

∴ Area of shaded region = Area of trapezium – (Total area of sectors)

= 350 – 154 = 196 cm^{2}

Hence, the required area of shaded region is 196 cm^{2}.

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