Q. 64.3( 27 Votes )

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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 = 350cm2

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 × r2

Area of the sector with central angle D = (1/2) × (D/180) × π × r2

Area of the sector with central angle B (1/2) × (B/180) × π × r2

Area of the sector with central angle C = (1/2) × (C/180) × π × r2

Total area of the sectors =   = 77 + 77 = 154

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

= 350 – 154 = 196 cm2

Hence, the required area of shaded region is 196 cm2.

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