Area of Triangle inside another Triangle

Question

I am stumped on the following question:

In the figure below $AD=4$ , $AB=3$ , and $CD=9$. What is the area of Triangle AEC?

I need to solve this using trigonometric ratios however if trig. ratios makes this problem a lot easier to solve I would be interested in looking how that would work. Currently I am attempting to solve this in the following way

$\bigtriangleup ACD_{Area}=\bigtriangleup ECD_{Area} + \bigtriangleup ACE_{Area}$

The only problem with this approach is finding the length of AE or ED. How would I do that ? Any suggestion or is there a better method

Answer 1

$AE+ED=AD=4$, and $ECD$ and $EAB$ are similar (right?), so $AE$ is to $AB$ as $ED$ is to $CD$. Can you take it from there?

Answer 2

Hint: $\bigtriangleup DCE \sim \bigtriangleup ABE$ as $BC$ is crossing parallel lines.