Question

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.   

Answer 1

Since, BFEC is a quarter of a circle.

Hence, BC = EC = 3.5 cm

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

Area of shaded region = Area of the trapezium ABCD − Area of the quadrant BFEC

`= 1/2xx("AB" + "DC")xx"BC" - 1/4xxpi("EC")^2`

`=1/2xx(3.5+5.5)xx3.5-1/4xx22/7xx(3.5)^2`

= 6.125 cm²

Hence, the area of the shaded region is 6.125 cm².