From each of the two opposite corners of a square of side 8cm, a quadrant of a circle of radius 1.4 cm is cut. Another circle of diameter 4.2cm is also cut from the centre as shown in figure. Find the area of the remaining (shaded) portion of the square.

Explanation

Side of square = 8 cm

Area of square` = (side)^2 = 8^2 = 64 cm^2`

Quadrant circle of radius r=1.4 cm
Area of quadrant circle `= (1/4)(pi xx r^2) =(1/4)xx (22/7) xx (1.4)^2 = 1.54 cm^2`

Diameter of bigger circle= 4.2 cm

`:.` Radius of bigger circle R= 2.1 cm

Area of bigger circle` = (pi xx R^2) = (22/7) xx (2.1)^2 =55.44 cm^2 `

area of the remaining portion of the square= Area of square - 2(Area of quadrant circle) - Area of bigger circle

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