Pentagonal tilings

Above shows a tessellation of identical pentagons.

Given that the side lengths of one of these pentagons are $a = 16, b = 8, c =4 \sqrt6 +4\sqrt2,8,8$ with angles $A=60^\circ, B=135^\circ,C=105^\circ,D=90^\circ,E=150^\circ$ . And it has an area of

$\large Y + Z\sqrt3$

for positive integers $Y$ and $Z$ . Find the value of $Y+Z$ .

Image Credit: Casey Mann.

Source: The Guardian .