Question

In the given figure, ABCD is a trapezium of area 24.5 cm², If AD || BC, ∠DAB = 90°, AD = 10 cm, BC = 4 cm and ABE is quadrant of a circle then find the area of the shaded region.

Answer 1

Area of trapezium `=1/2("AD" + "BC")xx"AB"`

`=>24.5 = 1/2(10+4)xx"AB"`

⇒ AB = 3.5 cm

Area of shaded region = Area of trapezium ABCD − Area of quadrant ABE

`= 24.5 - 1/4pi("AB")^2`

`= 24.5-1/4xx22/7(3.5)^2`

= 24.5- 9.625

= 14.875 cm² 

Hence, the area of shaded region is 14.875 cm²