8,9  [ Thales' Theorem and the Theorem of Proportional Segments ]

Diagonal $K M$ of trapezoid $K L M N$ is three times the length of segment $K P$ of this diagonal. Base $K N$ of the trapezoid is three times the length of base $L M$.

Find the ratio of the area of trapezoid $K L M N$ to the area of triangle $K P R$, where $R$ is the point of intersection of line $P N$ and side $K L$.
Draw through point $P$ a line parallel to the bases of the trapezoid, until it intersects side $K L$ at point Q.

## Answer

$32: 3$.