Book: RS Aggarwal - Mathematics
Chapter: 18. Area of Circle, Sector and Segment
Subject: Maths - Class 10th
Q. No. 39 of Exercise 18A
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39
In the given figure, a square OABC is inscribed in a quadrant OPBQ of a circle. IF OA = 20 cm, find the area of the shaded region. [Use π = 3.14]
Given:
OA = Side of square OABC = 20 cm
∵ Area of square = Side × Side
∴ Area of square OABC = 20 × 20 = 400 cm2
Now,
∵ Length of diagonal of square = √2 × Side of Square
∴ Length of diagonal of square OABC = √2 × 20 = 20√2 cm
⇒ Radius of the quadrant = 20√2 cm
∵ Area of quadrant = 
πr2
∴ Area of quadrant OPBQ = 
× 3.14 × 20√2 × 20√2
= 
× 400 × 2
= 3.14 × 200 = 628 cm2
Area of shaded region = Area of quadrant OPBQ – Area of square OABC = 628 – 400 = 228 cm2
Hence, the area of the shaded region is 228 cm2.
