Question

Let \[ A_{1}=\left\{(x, y):|x| \leqslant y^{2},|x|+2 y \leqslant 8\right\} \text { and } \] \( A_{2}=\{(x, y):|x|+|y| \leqslant k \} \). If \( 27\left(\right. \) Area \( \left.A_{1}\right)=5\left(\right. \) Area \( \left.A_{2}\right) \), then \( k \) is equal to :

Answer 1

A1=40/3 A2=2k²(yellow part is the area a1)