@TSS-Graviser Haha, yes, sometimes Prof. Loh takes a detour on his way to solving things. In fact, this is the whole design of the Daily Challenge course, in that you accidentally see concepts, theorems and formulas as a consequence of thinking about one little tricky problem.
I think he was trying to use this choice of explanation as a perfect example of similar triangles which are all packed efficiently and compactly into this one small kite. That's pretty neat, isn't it? There's another reason why learning about how to match the sides of the similar triangles and also calculate the ratios of their dimensions is really useful. What if you encounter in the future a question which isn't about area, but asks you to calculate the length of the line segment \(\overline{PC}\)? Or, for example, how do those kids answer those buzzer questions so blazingly fast without seemingly have to write anything down? Perhaps a question just gives you the value of one of the angles \(\angle a,\) the length of one diagonal, and then asks you mysteriously for the length of \(\overline{AD}.\) You can solve all these questions with just the understanding of the similar triangles in this diagram!
So yes, do take time to think about the "why" in math, and you'll reap great rewards with your mathematical intuition and understanding in the future.
Happy Learning ~~
