Question

find the area of shaded region where arc drawn with centre A,B,C,D intersects in point at mid point P,Q,R,S Of the side AB,BC,CD,DA respectively of a square ABCD of side 12cm

Answer 1

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....

Answer 2

See attached pic (Created my me)

Area of quadrant = $\bf\huge\frac{1}{4} \pi r^{2}$

Area of quadrant = $\bf\huge\frac{1}{4} \times3.14\times6^{2}$

Area of 4 quadrant = $\bf\huge 4\times\frac{1}{4} \times3.14\times36$

= 3·14 × 36

= 113·04 cm^2

Area of shaded region = Area of square  – Area of 4 Quadrant

= 144 – 113·04

Area of shaded region = 30·96 cm^2