MHB Area of Triangle ABC Given Dimensions

[maxkor]

In triangle ABC $AC=BD, CE=2, ED=1, AE=4$ and $\angle CAE=2 \angle DAB$. Find area ABC.

 

[jonah1]

Beer induced request follows.

In triangle ABC $AC=BD, CE=2, ED=1, AE=4$ and $\angle CAE=2 \angle DAB$. Find area ABC.

Please show us what you have tried and exactly where you are stuck.
We can't help you if we don't where you are stuck.

 

[maxkor]

This is what it looks like, but how to justify the red ones or maybe there is another way?

 

[HOI]

How did you get those?

 

[maxkor]

Geogebra...

 

[mrtwhs]

In your diagram, all three sides of $\triangle AEC$ are known. Using the law of cosines you get $2\alpha = \cos^{-1}(7/8)$ and $\alpha \approx 14.47751219^{\circ}$.

Continuing to use the law of cosines we get $AD=\dfrac{3\sqrt{10}}{2}$ and $AB=3\sqrt{6}$.

Finally, using the law of cosines on $\triangle ABD$ we get $\alpha \approx 71.170769^{\circ}$.

Your diagram is incorrect.