\((1)\)设不等式组\(\begin{cases}\begin{matrix}x\geqslant 0 \\ x+2y\geqslant 4\end{matrix} \\ 2x+y\leqslant 4\end{cases} \)所表示的平面区域为\(D\),则可行域\(D\)的面积为________.
\((2)\)已知\(\tan β= \dfrac{4}{3} \),\(\sin \left(α+β\right)= \dfrac{5}{13} \),其中\(α\),\(β∈(0,π)\),则\(\sin α\)的值为________.
\((3)\)已知函数\(f\left(x\right)=\left|{\log }_{3}x\right| \),实数\(m\),\(n\)满足\(0 < m < n\),且\(f\left(m\right)=f\left(n\right) \),若\(f(x)\)在\([m^{2},n]\)上的最大值为\(2\),则\(\dfrac{n}{m}=\)________.
\((4)\)过抛物线\({{y}^{2}}=4x\)的焦点的一条直线交抛物线与\(A\)、\(B\)两点,正三角形\(ABC\)的顶点\(C\)在抛物线的准线上,则\(\triangle ABC\)的边长为________.