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Question
In the given figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. [π = 3.14]
Solution
Area of the square ABCD =(Side)2
= 42
= 16 cm2
Area of the circle = πr2
Radius = 1 cm
Area = 3.14 × (1)2
= 3.14 cm2
Area of the quadrant of one circle`=1/4pi"r"^2`
`=1/4xx3.14xx1^2`
= 0.785 cm2
Area of the quadrants of four circles = 0.785 × 4 = 3.14 cm2
Area of the shaded region = Area of the square - Area of the circle - Area of the quadrants of four circles = 16-3.14-3.14 = 9.72 cm2
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