In the given figure, three sectors of a circle of radius 7 cm, making angles of 60°, 80° and 40° at the centre are shaded. Find the area of the shaded region.

(CBSE 2012)

Given:

Radius of circle = 7 cm

Let the sectors with central angles 80°, 60° and 40° be S₁, S₂, and S₃ respectively.

Then, the area of shaded region = Area of S₁ + Area of S₂ + Area of S₃ …………………….. (i)

∵ Area of sector = × πr²

∴ Area of S₁ = × × 7 × 7

= cm²

Similarly, Area of S₂ = × × 7 × 7

= cm²

and Area of S₃ = × × 7 × 7

= cm²

Thus, using (i), we have

Area of shaded region = + +

=

= = 77 cm²

Hence, the area of shaded region is 77 cm².