# Pentagonal tilings

Geometry Level 4

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 $$Y+Z$$.

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