ABCDEF is a regular hexagon with sides of length h cm.

A square PQRS is drawn inside the hexagon, with PQ parallel to AB, SR parallel to ED, and vertices PQRS lying on FA, BC, CD and EF respectively.

The area of PQRS is 4 cm².

What is the exact value of h?

PS The first version of this challenge was about a square and a pentagon which is why it is called Squentagon. It's a great word, so when the shape was changed, the name stayed the same.