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Sum

In Figure, find the area of the shaded region [Use π = 3.14]

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#### Solution

From the symmetry of the given figure, we have

Let the radius of semicircle, r = `d/2 = 4/2 = 2cm` (Diameter of semicircle, d = `14/2 - 3` = 4 cm )

Let the side of small square = a = 4 cm (Side = Diameter of semicircle

Area of square ABCD = (Side)^{2} = (A)^{2} = (14)^{2} = 196cm^{2}Area of small square PQRS = (Side)^{2} = (a)^{2} = (4)^{2} = 16cm^{2}

Area of 4 Semicircle = 4 x `1/2 pir^2`

= 4 x `1/2 xx 3.14 xx 2^2 = 25.12 cm^2`

∴ Required area = ( Area of big square – Area of small square – Area of 4 semicircles ) = ( 196 - 16 - 25.12 ) = 154.88 cm^{2}

Concept: Circumference of a Circle

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