Find the area of shaded region in fig. Where area is drawn with centres A,B,C and D intersects in pair at mid-points P,Q,R, and S of the sides AB,BC,CD and DA respectively of a square ABCD of side 12 cm
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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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