Question

From a thin metallic piece in the shape of a trapezium ABCD in which AB || CD and $\angle$ BCD = ${90}^{\circ }$, 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.

Answer 1

A thin metalic piece in the shape of trapezium ABCD in which AB || CD and BCD = 90° a quarter circle BFEC is removed as shown in figure .

Given , AB = BC =3.5 cm and DE = 2cm

here you can see that , CE = CB = 3.5 cm { because CE and BC are the radii of quarter circle BFEC }
so,DC = DE + EC = 2cm + 3.5 cm = 5.5 cm

now, area of remaining part of trapezium ABCD = area of trapezium ABCD - area of quarter circle BFEC

= 0.5{ AB + DC } × BC - π(BC)²

= 0.5{3.5 cm + 5.5cm } × 3.5cm - π(3.5cm)²
= 4.5cm × 3.5cm - cm²
= 6.125 cm²