Jenia is a very talented girl. She got homework from school. She is such a nerd who cries if she can’t complete her homework every day. Yesterday her math teacher taught her about circles, semi-circles, square etc. gave her a geometric shape and asked her to find the area and perimeter of the shaded region given the area A of the Square where four quarter circles with the same radius are inside the square. She has been thinking and thinking for the whole evening and eventually slept with frustration. Can you help her to find the area and perimeter of the shaded region given the area of the square?

This is a companion discussion topic for the original entry at https://toph.co/p/jenia-s-homework