Question

PQRS is a rectangle in which PQ is 20 QR is 10 cm. A semicircle is drawn with centre O with radius 10root 2 cm and it passes through A and B. Find the shaded region.

Answer 1

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Answer 2

Answer:

the real answer is 142.86 approx

Explanation:

Sol :

Given that ABCD is a rectangle of length =20 cm

                                                       breadth = 10 cm

area of rectangle = l x b = 20 x 10 = 200 cm 2

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 the sector - the area of OAB ]

                                   = 200 -[ 157.1428 - 100]

                                  = 200 - 57.1428

                                  = 142.8572 cm2 .