I am not going to show all calculations, but feel free to ask questions and post your work to be checked.

I don't think we can tell for sure how Crawford did it Maybe he used Monte Carlo method.

You can find AC and AD using the law of cosines. Then you can find angles BAC and DAE using the law of sines. This way, you can find angle CAD. Then you can find the areas of triangles BAC, CAD and DAE using cross product.