For a triangle \(XYZ\), we use \([XYZ]\) to denote its area.

Let \(ABCD\) be a square with side length 1. Points \(E\) and \(F\) lie on \(BC\) and \(CD\), respectively, in such a way that angle EAF = 45 degrees. If [CFE] = \(1/19\), what is the value of [AEF]?

I know that heureka solved a similar problem with [CFE] = 1/9, and I tried to follow that solution. Here is the link: https://web2.0calc.com/questions/for-a-triangle-xyz-we-use-xyz-to-denote-its-area. I tried to follow his/her solution, but I still made a mistake somewhere. Can someone please help? Thank you very much!

Exodush21 Sep 10, 2021