Circle moving around hexagon

There is an equilateral pentagon whose length of one side is 4 cm.

As shown in a figure, five arcs passing through each vertex with a radius of 4 cm are drawn in the inside of the equilateral pentagon.

A disk 1 cm in diameter moves one round touching five arcs.

In this case, find the area of the portion along which the disk passed. The answer should be rounded off a 2nd decimal place and should be until the 1st decimal place.

Noted that an equilateral pentagon is a pentagon with the same length of all the sides and an equal size of an angle and arc is a part of the circumference.

Answer