3.12 is one of the harder questions with area transformation.  To start, let $Q$ be the midpoint of $CD$ and try to connect some midpoints to form parallel lines, then transfer the areas around. 

3.13 Use homothety: verify that triangles $ABC$ and $O_1O_2O_3$ are homothetic with center $P$.

3.14 Use translation to move the lines so that all the lines pass through the same point.

3.15 (2) You need to solve (1) first by translating the segments together; this process actually give you some ideas on how to cut up the new triangle and calculate the areas. In fact, the question only provides that the triangle $ABC$ has area 10, so that is the only information you need for the new triangle's area.