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From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in the given figure. Find the area of the remaining portion of the square [Use Π = 22/7]

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#### Solution

Each quadrant is a sector of 90° in a circle of 1 cm radius.

Area of each quadrant = `90^@/360^@pir^2`

`= 1/4xx22/7xx(1)^2 = 22/28 cm^2`

Area of square = (Side)^{2} = (4)^{2} = 16 cm^{2}

Area of circle = π*r*^{2} = π (1)^{2}

`= 22/7 cm^2`

Area of the shaded region = Area of square − Area of circle − 4 × Area of quadrant

` = 16 -22/7 - 4 xx 22/28`

`= 16-22/7-22/7 = 16 - 44/7`

`= (112-44)/7 = 68/7 cm^2`

Concept: Areas of Combinations of Plane Figures

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