Let the area enclosed by the lines \( x+y=2 \), \( y=0 \), \( x=0 \) and the curve \( f(x)=\min\!\left\{x^{2}+\dfrac{3}{4},\,1+[ x ] \right\} \) where \( [ x ] \) denotes the greatest integer \( \le x \), be \( A \). Then the value of \( 12A \) is ________.
