Polygons ratio

ABCD is a parallelogram.

From each vertex, we join the middle of the 2 opposites sides
F is the middle of BC
E is the middle of CD
We draw the lines AF and AE

We draw thus 8 lines which define an octogon.

What is $\frac{Area(Octogon)}{Area(Parallelogram)}$

Give your answer rounded to 10 digits after the decimal point