Q) Reeti prepares a rakhi for her brother Ronit.  The Rakhi consists of a rectangle of length 8 cm and breadth 6 cm inscribed in a circle as shown in the figure. Find the area of the shaded region. (Use = 3.14)

Ans:

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Since the rectangle is inscribed inside the circle, its diagonals will pass through the center of circle and will be equal to circle’s diameter.

From the given information on rectangle, we can write:

(diagonal)² = 6² + 8²

diagonal = 10 cm = diameter of circle

    Radius of circle, r = 5 cm

Now, area of circle  = 3.14 x 5 x 5 = 78.5 cm²

Area of rectangle = 6 x 8 = 48 cm²

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

= 78.5 – 48 = 30.5 cm²

 Therefore, Area of shaded region is 30.5 cm²