From a thin metallic piece in the shape of a trapezium ABCD in which AB ∥ CD and ∠BCD = 90°, a quarter circle BFEC is removed. Given, AB = BC = 3.5 cm and DE = 2 cm, calculate the area of remaining (shaded) part of metal sheet.

Given:

AB ∥ CD

∠BCD = 90°

AB = BC = 3.5 cm = EC

DE = 2 cm

DC = DE + EC = 2 + 3.5 = 5.5 cm

Area of Trapezium = × Sum of Parallel Sides × h

= × (AB + DC) × BC

= × (3.5 + 5.5) × 3.5

= × 9 × 3.5

= 15.75 cm^{2}

Area of Quadrant BFEC = × πr^{2} = × × 3.5 × 3.5

= 9.625 cm^{2}

Thus, Area of remaining part of metal sheet

= Area of Trapezium – Area of Quadrant BFEC

= 15.75 – 9.625 = 6.125 cm^{2}

__Hence, the area of the remaining part of metal sheet is 6.125 cm ^{2}.__

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