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Find the Area of the Shaded Region Use π = 3.14 - Mathematics

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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 = 196cm2
Area of small square PQRS = (Side)2 = (a)2 = (4)2 = 16cm2

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 cm2

Concept: Circumference of a Circle
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