# Pentagonal tilings

**Geometry**Level 4

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 \(Y+Z\).