From each corner of a square of side 4cm a quadrant of a circle of radius 1cm is cut and also a circle of diameter 2cm is cut as shown in fig. Find the area of the remaining portion of the square.
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Solution
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Area of shaded region = Area of square ABCD− Area of 4 quadrants − Area of circle with diameter 2 cm Area of square =4×4=16cm2
Area of sector =θ360×π×r2
Area of 4 quadrants =4×90360×π×1×1 =3.14cm2 Area of circle=π×r2=π×1×1 =3.14cm2 ∴ Area of shaded region =16−6.28=9.72cm2
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