Question

calculate the area of shaded region common between two quadrants of circles of radius 8cm each ( as shown in the given figure )

Answer 1

Answer:

36.57 cm²

Step-by-step explanation:

Find the area of the square:

Area = Length x Length

Area = 8 x 8 = 64 cm²

Find the area of one quadrant:

Area = 1/4 πr²

Area = 1/4 π (8)² = 50.29 cm²

Find the area of the square not covered by 1 quadrant:

Area = 64 - 50.29 = 13.71 cm²

Find the area of the shaded region:

Shaded Area = Area of the square - 2(area not covered by the quadrant)

Shaded Area = 64 - 2(13.71) = 36.57 cm²

Answer: The area is 36.57 cm²

Answer 2

HELLO DEAR,

GIVEN;- radius (R) = 8cm as, Circle is in the square so, θ = 90°

now, see in figure,
area of shaded region = 2(area of quadrant) - area of square,

now, area of quadrant = θ/360πR²

so, 90/360*π(8)²

=> 1/4(22/7)(64) = (352/7)cm²

then 2(area of quadrant) = 2(352/7) = 704/7cm²

and ,
area of square of side 8cm = side² = (8)² = 64cm²


thus, area of shaded region = (704/7 - 64)cm²

=> (704 - 448)/7cm²

=> 256/7cm²

=> 36.57cm²



I HOPE IT'S HELP YOU DEAR,
THANKS