Question

In the given figure, ABCD is a rectangle of 20 cm * 10 cm. A semicircle is drawn with centre O . The radius is 10 root 2cm and it passes through A and B .Find the area of the shaded region.

Answer 1

Given that ABCD is an rectangle of length =20 cm

Breadth = 10 cm

Area of rectangle = l x b = 20 x 10 = 200 cm²

Here  ∠AOB = 90°

OAEB is an sector of radius OA = OB = 10√2

Area of sector = (1/2) r2 θ

= (1/2) x 10√2 x10√2x π/2.= 157.1428 cm²

area of OAB = (1/2) x 10√2 x10√2 = 100 cm²

area of shaded region =  area of rectangle ABCD -[ Area of sector - area of OAB ]

= 200 -[ 157.1428 - 100]

= 200 - 57.1428

= 142.8572 cm²