My Russian Instructor at DLI was a history buff. He talked about how Russian words were created from a root/base, with one or more prefixes or suffixes added as needed to convey the meaning. (I owned a book on Russian roots, it helped a lot).
Anyways, Red/красный was considered the most beautiful/красивый color so it shares the same root.; but, (according to him), here is the interesting part:
When Красная Площадь was built, it was called that, but it meant Beautiful Square...
The meanings of the two words swapped over the years.
Roots of the Russian Language - An Elementary Guide to Wordbuilding
When I came across a new word in the newspaper I'd look up the root and compare the difference in meaning when the prefix and/or suffix was changed. A simple example early in Duo's Russian course: писать, записать and написать
Off the top of my head there's also: списать, описать, прописать, подписать, выписать и расписать.
Once you become familiar with the more common prefixes and suffixes and start to see more roots, your ability to 'guess' from context goes way up.
Only Красная is a proper name [I'm wrong here], площадь is just a square. It is not capitalized in wiki as well: https://ru.wikipedia.org/wiki/%D0%9A%D1%80%D0%B0%D1%81%D0%BD%D0%B0%D1%8F_%D0%BF%D0%BB%D0%BE%D1%89%D0%B0%D0%B4%D1%8C