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Find the area of the shaded region in fi...

Find the area of the shaded region in figure, in figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-point P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD. (use `pi = 3.14`)

Text Solution

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Given, side of a square BC = 12cm
Since, Q is a mid - point of BC.
`:.` Radius = `BQ= (12)/(2)=6cm`
Now , area pf quadrant `BPQ = (pir^(2))/(4)=(3.14xx(6)^(2))/(4) = (113.04)/(4)cm^(2)`
Area of four quadrants = `(4xx113.04)/(4)=1123.04cm^(2)`
Now, area of square ABCD = `(12)^(2)=144cm^(2)`
`:.` Area of the shaded region = Area of square- Area of four quadrants
= `144 - 113.04 = 30.96 cm^(2)`
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