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In Figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)

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In Figure, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)

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Side of square = OA = AB = 20 cm

Radius of the quadrant = OB

OAB is right angled triangle

By Pythagoras theorem in ΔOAB,

OB= AB2+OA2

⇒ OB= 20+202

⇒ OB= 400 + 400

⇒ OB= 800

⇒ OB= 20√2 cm

Area of the quadrant = (πR2)/4 cm

= (3.14/4) × (20√2)cm= 628 cm2

Area of the square = 20 × 20 = 400 cm2

Area of the shaded region = Area of the quadrant – Area of the square

= 628 - 400 cm

= 228cm2

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