## Book: RS Aggarwal - Mathematics

### Chapter: 18. Area of Circle, Sector and Segment

#### Subject: Maths - Class 10th

##### Q. No. 43 of Exercise 18A

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43
##### Find the area of the shaded region in the given figure, if ABCD is a rectangle wit sides 8 cm and 6 cm ad O is the centre of the circle.

Given:

Length of rectangle = 8 cm

Breadth of rectangle = 6 cm

Area of rectangle = length × breadth

= 8 × 6 = 48 cm2

Consider ABC,

By Pythagoras theorem,

AC2 = AB2 + BC2

= 82 + 62 = 64 + 36 = 100

AC = √100 = 10 cm

Diameter of circle = 10 cm

Thus, radius of circle = = 5 cm

Let the radius of circle be r = 5 cm

Then, Area of circle = πr2

= × 5 × 5 = = = 78.57 cm2

Area of shaded region = Area of circle – Area of rectangle

= 78.57 - 48

= 30.57 cm2

Hence, the area of shaded region is 30.57 cm2.

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