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Question
Find the area of the shaded region in the figure If ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. (Take π= 3.14)
Solution
Here, diagonal AC also represents the diameter of the circle.
Using Pythagoras theorem:
AC = `sqrt(AB^2 + BC^2)`
AC = `sqrt(8^2 + 6^2)`
AC = `sqrt(64 + 36)`
AC = `sqrt100`
AC = 10
RAdius of the circle, OC = `"AC"/2 = 5 "cm"`
Area of the shaded region = Area of the circle - Area of rectangle
= `pi"r"^2 - "AB"xx"BC"`
= `pi ("OC")^2 - "AB"xx"BC"`
= 3.14 x 52 - 8 x 6
= 78.5 - 48
= 30.5
Therefore, the area of shaded region is 30.5 cm2 .
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