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Home »  In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)
 In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)
Areas Related To Circles | CBSE | Class 10 | Maths | NCERT
 In Fig. 12.31, a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)

Solution:

Squares’ side = AB = OA = 20 cm

Quadrants’ radius = OB

The OAB triangle is a right-angled triangle.

Using the Pythagoras theorem in ΔOAB,

OB2 = AB2+OA2

⇒ OB2 = 202 +202

⇒ OB2 = 400+400

⇒ OB2 = 800

⇒ OB= 20√2 cm

Quadrants’ area = (πR2)/4 cm2 = (3.14/4)×(20√2)2 cm2 = 628cm2

The area of the square = 20×20 = 400 cm2

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

= 628-400 cm2 = 228cm2

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