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.
