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Question
Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle.
Solution
In right triangle ABC
AC2 = AB + BC2
= 82 + 62
= 64 + 36
= 100
∴ AC2 = 100
⇒ AC = 10 cm
Area of the shaded region = Area of circle − Area of rectangle OABC
`=> pi("OA")^2 -"AB"xx"BC"`
`⇒ 22/7xx(5)^2-8xx6`
= 78.57 - 48
= 30.57 cm2
Hence, the area of the shaded region is 30.57 cm2.
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