Find the area of the shaded region where area drawn with centres a,b,c and intersect in pairs at mid point of pars of the sides ab bc cd da resp. of the square abcd of side 12 cm (pie=3.14)
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Given :
Side of square = 12 cm
In figure, Four quadrants are included in the four sides of the square PAS, PBQ,RCQ, RDS.
Radius of the circle(r) = 12/2 cm = 6 cm
Area of the square ABCD = side × side = 12² = 144 cm²
Area of 1 quadrant = (π r²)/4 cm² = (3.14 × 6²/4 cm²
= 3.14 × 36 / 4 = 3.14 × 9 = 28.26cm²
Area of 4 quadrants = 4 × 28.26 cm² = 113.04 cm²
Area of the shaded region = Area of the square ABCD – Area of 4 quadrants
= 144 cm² – 113.04 cm² = 30.96 cm²
Hence, the area of the shaded region is 30.96 cm².
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