The area of the designed region in figure, common between the two quadrants of the circles of radius 10 cm each is  (use $\mathrm{\pi }$ = 3.14 ) 

: Radius of the circle (r) = side of the square = 10 cm

  Area of shaded region $=2\left[\text{Area of sector ABD –Area of }\Delta \text{ABD}\right]$

  Area of sector ABD $=\frac{x}{360}\times \pi r^2$

   $=\frac{90}{360}\times \left(3.14\right)\times \left(100\right)$

   $=\frac{1}{4}\times 314=78.5c{m}^2$

 $Ar\left(\Delta ABD\right)=\frac{1}{2}\times AB\times AD$

  $=\frac{1}{2}\times 10\times 10=50c{m}^2$

 $\therefore$ Area of shaded region $=2\times \left[\text{Area of sector ABD – Area of }\Delta \text{ABD}\right]$

 $=2\times [78.5-50]$

 $=2\times 28.5=57c{m}^2$