find the area of the shaded region in fig.where drawn with centre A, B ,C,D and d intersect in pair at midpoint P,Q,R and S of the side AB,BC,CD,DA respectively of a squre ABCD of side 12cm
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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.
HOPE THIS WILL HELP YOU.....
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.
HOPE THIS WILL HELP YOU.....
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