Let a triangle be bounded by the lines $L_{1 i} 2 x+5 y=10 ; L_{2 i}-4 x+3 y=12$ and the line $L_3$, which passes through the point $P(2,3)$, intersect $L_2$ at $A$ and $L_1$ at $B$. If the point $P$ divides the line-segment $A B$, internally in the ratio $1: 3$, then the area of the triangle is equal to