Riddle of the month. How do i show that the triangles have the same area?

[AlgebraSystem]

Look at the triangle in the picture. E represents the midpoint of the line DC and P is the intersection of the diagonal AC and line BE. How do I show that the triangles BCP and CDP have the same area and how do I calculate the proportion of the area of the triangle ABP with respect to the area of the whole parallelogram?

I actually have no idea how to show it. I had tried to show about the similarity, but unfortunately not successful. I hope you can help me. Best regards.

 

[tkhunny]

Initial Thought: I'm leaning toward Heron's Formula as possibly instructive.

 

[Dr.Peterson]

How do I show that the triangles BCP and CDP have the same area?

Look at BCP and CDP as sharing the base CP. How do their altitudes compare?

and how do I calculate the proportion of the area of the triangle ABP with respect to the area of the whole parallelogram?

Use similar triangles ABP and ECP. Use the result to compare triangles ABP and ABC.

 

[jonah2.0]

Beer soaked ramblings follow.
This ought to be renamed as Trivial Riddle of the month.
A(0,0), B(8,0), C(11,3), D(3,3), E(7,3), P(?,?)
For P's coordinates, you merely have to find the intersection of y-3=(3-0)/(11-0)*(x-11) and y-3=(3-0)/(7-8)*(x-7).

 

[Dr.Peterson]

This ought to be renamed as Trivial Riddle of the month.
A(0,0), B(8,0), C(11,3), D(3,3), E(7,3), P(?,?)
For P's coordinates, you merely have to find the intersection of y-3=(3-0)/(11-0)*(x-11) and y-3=(3-0)/(7-8)*(x-7).

I'm assuming that the specific coordinates shown are not part of the problem; all conditions should be stated in words, and nothing assumed from the picture -- especially here, where if the coordinates could all be assumed, we wouldn't need most of the words. (Of course, it can be argued that your coordinate system can be imposed without loss of generality ... up to a point.)