518. In triangle $ABC$, a point $M$ is taken on side $AC$, dividing it in the ratio $AM: MC=1: 3$. Find the area of triangle $ABM$, if the area of triangle $ABC$ is 1.
$\triangle$ In triangles $A B C$ and $A B M$, there is a common height dropped from point $B$, and the sides $A C$ and $A M$, onto which it is dropped, differ by a factor of four. Therefore, the area of triangle $A B M$ is $1 / 4 . \triangleleft$

The same reasoning shows that if one side of a triangle is increased or decreased by a factor of $k$, while keeping the other side and the angle between the sides unchanged, the area of the triangle will also increase or decrease by the same factor of $k$.