2018 Pascal Problem 20

In the diagram, PQRST is a pentagon with PQ = 8, QR = 2, RS = 13, ST = 13, and TP = 8. Also, \angle TPQ = \angle PQR = 90^\circ. What is the area of pentagon PQRST?

\textbf{(A)}\ 76\quad \textbf{(B)}\ 84\quad \textbf{(C)}\ 92\quad \textbf{(D)}\ 100\quad \textbf{(E)}\ 108

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.