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From each of the two opposite corners of a square of side 8 cm, a quadrant of a circle of radius 1.4 cm is cut. Another circle of radius 4.2 cm is also cut from the centre as shown in Fig.. Find the area of the remaining (shaded) portion of the square.(use π = \(\frac{22}7\)).

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Given, 

Side of square = 8 cm 

Radius of quadrant circle = 1.4 cm 

Radius of inner-circle = 4.2 

Area of square = (side)2 = 82 = 64 cm 

Area of one quadrant of circle = \(\frac{θ}{360}\timesπr^2\)

Area of one quadrant of circle = \(\frac{90}{360}\times\frac{22}7\times1.4\times1.4\) = 1.54 cm2

So, 

Area of 2 quadrant = 2×1.54 = 3.08 cm2 

Area of inner circle = πr2 = 3.14 × 4.2 × 4.2 = 55.44 cm

Area of shaded portion = area of square – (area of quadrants + area of inner circle) 

= 64 – (3.08 + 55.44) 

= 64 – 58.52 = 5.48 cm2

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