Let \( A(1, 1), \; B(-4, 3), \; C(-2, -5) \) be vertices of a triangle \( ABC \). \( P \) be a point on side \( BC \), \( \Delta_{1} \) and \( \Delta_{2} \) be the areas of triangles \( APB \) and \( ABC \), respectively. If \( \Delta_{1} : \Delta_{2} = 4 : 7 \), then the area enclosed by the lines \( AP \), \( AC \) and the \( x \)-axis is:
