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Question
In the given figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region. [Use Π = 22/7]
Solution
Area of each of the 4 sectors is equal to each other and is a sector of 90° in a circle of 7 cm radius.
Area of each sector = `90^@/360^@ xx pi(7)^2`
`=1/4xx22/7xx7xx7`
`= 77/2 cm^2`
Area of square ABCD = (Side)2 = (14)2 = 196 cm2
Area of shaded portion = Area of square ABCD − 4 × Area of each sector
`196 - 4 xx 77/2 = 196 - 154`
`= 42 cm^2`
Therefore, the area of shaded portion is 42 cm2.
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