 ## 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

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.

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