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 \pi = 3.14)

Reeti prepares a rakhi CBSE 10th Board




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

\therefore diagonal = 10 cm = diameter of circle

\therefore    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

\therefore     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

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