In the figure, the area of the shaded region is:

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Solution

Q.
In the figure, the area of the shaded region is:

1 $3 π {cm}^{2}$

2 $6 π {cm}^{2}$

3 $9 π {cm}^{2}$

4 $7 π {cm}^{2}$

Ans.
(1)

$S i n c e A B ∥ C D, ∠ B A D + ∠ A D C = 180 ° (C o - i n t e r i o r a n g l e s) \Rightarrow ∠ B A D + 60 ° = 180 ° \Rightarrow ∠ B A D = 120 ° \Rightarrow θ = 120 ° and r = 3 cm ∴ Area of shaded region = \frac{θ}{360 °} \times {πr}^{2} = \frac{120 °}{360 °} \times π \times (3)^{2} = \frac{1}{3} \times 9 π = 3 π {cm}^{2}$

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