JMO 1995 Problem 3

Given a convex pentagon $ABCDE.$ Let $S,R$ be the intersection points of $AC$ or $AD$ and $BE$ respectively, and let the intersection points $T,P$ of $CA$ or $CE$ and $BD$ respectively.Let $Q$ be the intersection point of $CE$ and $AD.$ If all of $\triangle{ASR},\ \triangle{BTS},\ \triangle{CPT},\ \triangle{DQP},$ and $\triangle{ERQ}$ have the area of $1,$ then find the area of the following pentagons.

(1) The pentagon $PQRST.$ (2) The pentagon $ABCDE.$