- to solve something by using reasoning
- to clear something up
- to understand why someone acts in a certain way
- it is a colloquial phrase and is not often used in a formal conversation
- It doesn't matter how long it takes. I am going to figure out this math problem.
- He was able to figure out who the killer was pretty quickly. That is why I like that show.
- She is going to figure out that you lied to her.
- Were you able to figure out the new IT system at work?
- I am having trouble figuring him out. He is always so mysterious.
- She is a difficult person to figure out. Sometimes she is so rude to me.
- I can't figure out why my new colleague is always eating.
Relating to discovering something the phrase seems to have originated in the early 1900s. I can't figure her out.
Related to solving a problem it has been used since the 1800s. Please help me figure out this math problem.
It is a phrasal verb if used in a context where something literally needs to be figured out. If it is used in a more figurative fashion it is an idiom.