Puzzle #61: what is the side length of the square?

Spoleto Cathedral is the cathedral of the Archdiocese of Spoleto-Norcia created in 1821, previously that of the diocese of Spoleto, and the principal church of the Umbrian city of Spoleto, in Italy. It is dedicated to the Assumption of the Blessed Virgin Mary.

The church is essentially an example of Romanesque architecture, with a nave and two side-aisles crossed by a transept, although subsequently modified. It was built from the second half of the twelfth century after the city had been devastated by Frederick Barbarossa’s troops, over an area where there had previously stood an earlier cathedral, dedicated to Saint Primianus and destroyed by the emperor. A notable external porch and the belfry were added in the fifteenth and sixteenth century respectively.

Puzzle

The picure below represents a visualization of a Terracotta tile flooring mosaic in Santa Maria Assunta Cathedral dating from the 12th century

You know that the small circles have all the same dimension and the radius of the bigger circle is twice the small one

The value of the red diagonal is 4√2

Can you find out the side length of the green square?

Have fun!