Question

In the following figure, the area of the shaded region is
(a)3π cm²
(b)6π cm²
(c)9π cm²
(d)7π cm²​

Answer 1

Answer:

The area of the shaded region is 3π cm² .

Among the given options option (a) 3π cm² is the correct answer.

Step-by-step explanation:

Given :

Radius of a circle , r = 3 cm

∠C = ∠B = 90° , ∠D = 60°  

∠A + ∠B + ∠C +  ∠D = 360°  

∠A + 90° + 90° + 60° = 360°

∠A + 240° = 360°

∠A = 360° - 240°

∠A = 120°

θ = 120°  

Area of the shaded region, A =  Area of a sector  

A = θ/360 × πr²

A = 120°/360° × π × 3²

A = ⅓ × 9π

A = 3π cm²

Area of the shaded region = 3π cm²

Hence, the area of the shaded region is 3π cm² .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer :-

→ Option (a) ; 3π cm² .

Step-by-step explanation :-

We have,

→ ∠ABC = 90° .

→ ∠BCD = 90° .

→ ∠ADC = 60° .

AND, PA( r ; radius ) = 3 cm .

Then, ∠BAD = 360° - ( ∠ABC + ∠BCD + ∠ADC ) .

= 360° - ( 90° + 90° + 60° ) .

= 360° - 240° .

= 120° .

Now,

∵ Area of shaded reason = area of sector of circle PAQ .

$\because$ Area of sector = [ ( θ/360 ) × πr² ] cm² .

= [ ( 120/360 ) × π(3)² ] cm² . { Here θ = 120° } .

= [ 1/3 × π × 9 ] cm² .

= 3π cm² . [ Option :- (a) ] .

Hence, it is solved .