Area Under The Curves

Let

\({A_1} = \left\{ {(x,y):|x| \le {y^2},|x| + 2y \le 8} \right\}\) and

\({A_2} = \left\{ {(x,y):|x| + |y| \le k} \right\}\). If 27 (Area A₁) = 5 (Area A₂), then k is equal to :