# area of traingle

#### maxkor

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

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#### jonah

##### Active member
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.

#### maxkor

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

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#### Country Boy

##### Well-known member
MHB Math Helper
How did you get those?

Geogebra...

#### mrtwhs

##### Active member
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 $\alpha \approx 71.170769^{\circ}$.