Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image>Polygon ABCD ~ polygon AEFG, $m\angle AGF = 108$, GF = 14, AD = 12, DG = 4.5, EF = 8, and AB = 26.
Find the perimeter of trapezoid AEFG