I want to make a plane like a trike. I have a design and some knowledge about plane requirements.
You don't need to know much aerodynamics to build a plane if you follow plans for an existing design that somebody else has engineered and validated, and you don't make any modifications.
If you are trying to design and build something new, even if superficially similar to existing aircraft, then yes you will need to study aerodynamics and other aspects of aeronautical engineering. This doesn't necessarily need to be formal academic study but there is a substantial body of knowledge that you will have to learn in order for your project to be safe and successful.
It's not compulsory as in there's no law requiring you to have studied aerodynamics in order to design an aircraft.
It is however exceedingly hard to design an efficient and safe (and able to fly at all) aircraft without a thorough understanding of aerodynamics, so studying the field is a very good idea.
What set the Wright brothers apart from many others who were trying to design and build flying machines around that time is that they went through the effort of studying and analysing other flying things, like birds, and also looked at the partially successful attempts by people like Otto Lilienthal and learned from what worked for those machines and what didn't.
Only when they had what they considered an understanding of how things worked did they set out to build their own models, gliders, and eventually powered aircraft.
Had they just set down behind their workbenches and start churning out parts to put together with little thought as to their correct shape, size, and such, they'd have failed like so many before (and since).
No, aerodynamics study is not compulsory for building an aircraft, or parts of it.
Some aircraft have been built by thousands of people, none of whom were asked for their diplomas.
But if you want to legally fly what you've build, in USA airspace, then you must choose which category it falls into and what laws apply to it. https://www.eaa.org/eaa/aircraft-building/building-your-aircraft/getting-started/selection-articles/faa-51-rule