Answer :

We can clearly see that the figure comprises of a rectangle and a semi-circle.

Name the rectangle ABCD. Name the point where the

rectangle and the semi-circle meets as E.

Take any point F on the semi-circle, then we have

the semi-circle as EFD.

Now, area of the figure = Area of the semi-circle + Area of the rectangle.

Here, from the figure, Radius of the semi-circle = r = 6 - 4 = 2 m

∴ Area of the semi-circle = πr^{2}/2 = 4π/2 = 2π

Also, area of the rectangle = Length × Breadth

= AB × BC

= 4 × 8 = 32 m^{2}

∴Area of shaded region = Area of rectangle ABCD + Area of semi-circle DEF

= (32 +2π) m^{2}

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