Compute area of a trapezoid

Question

In the figure, $ABCD$ is a trapezoid of bases $AB$ and $DC$. $P$ is the midpoint of $CE$. If the area of $\triangle DFC = 3$ and the area of $AEPF = 21$, compute the area of $AECD$.

My try

I made a system of equation naming the areas of $AFD$ and $PFC$ $a$ and $b$, then I drew the height of $AECD$ and used it to compute the area of the triangles $\triangle ADC$ and $\triangle AEC$ and the trapezoid $AECD$ in function of my two variables $a$ and $b$, but I found that if I relation those areas, it's circular (I got an expression of the form $0=0$). I'm aware that I have to use the fact that $P$ is the midpoint of $CE$ but I don't know how.

Any hints are appreciated.

Answer 1

$x + 2y = 21$

$\dfrac {3 + 2x}{3} = \dfrac {y}{x}$

Eliminating y from the above to get a quadratic in x, and x = ... = 3.

Answer 2

HINTS:

P is the midpoint hence EBCD is a parallelogram.

The triangles ACD, BCD and EBC have equal area.