Find the area of the shaded region.

We know that : If in a Circle of Radius 'r', an Arc of length 'l' subtends an Angle 'θ' radian at the Centre then Relation between them is given by :

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Given : The Arc Length of the Larger Sector = 12 m

Given : θ = 1 radian

Given : The Arc Length of the Smaller Sector = 8 m

The Way to look at this Solution is to Realize that : If we Subtract the Area of Smaller Sector from the Area of Larger Sector, we will end up with the Area of the Shaded Region.

We know that : Area of a Sector with Radius r is given by :

where : θ is the Angle subtended (in Radians)

Area of the Shaded Region = (72 - 32) = 40m²

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction