Four Leaf Clover

The diagram shows four equal discs and a square. What is the perimeter of the figure?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Problem

Image
Four Leaf Clover


The diagram shows four equal discs and a square. Each disc touches its two neighbouring discs. Each corner of the square is positioned at the centre of a disc. The side length of the square is $\frac{2}{\pi}$. What is the length of the perimeter of the figure?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.