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 \(Y+Z\).

Image Credit: Casey Mann.
Source: The Guardian.

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