From a thin metallic piece in the shaped of a trapezium ABCD in which `AB||CD` and `/_BCD=90^(@)`,a quarter circle BFEC is removed. Given, `AB=BC=3.5cm` and `DE=2cm` calculate the area of remaining (shaded) part of metal sheet.

Explanation

Given : `AB=BC=3.5cm` and `DE=2cm`

Height of trapezium `h = BC = 3.5cm`

bases of trapezium are AB and CD

As `BC= EC` (radius of quarter circle)

`:. CD = DE+EC = 2cm+3.5cm = 5.5cm`

Area of a trapezium ABCD = `1/2(AB+CD) xx h`

`:.`Area of a trapezium ABCD =` (1/2) xx (3.5+5.5) xx 3.5 =15.75 cm^2`

Area of quarter circle =` (1/4) xx pi xx r^2 `

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