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 cm^{2}

Consider ABC,

By Pythagoras theorem,

AC^{2} = AB^{2} + BC^{2}

= 8^{2} + 6^{2} = 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 = πr^{2}

= × 5 × 5 = = = 78.57 cm^{2}

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

= 78.57 - 48

= 30.57 cm^{2}

__Hence, the area of shaded region is 30.57 cm ^{2}.__

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