2020 Cayley Problem 10

In the diagram, pentagon PQRST has PQ = 13, QR = 18, ST = 30, and a perimeter of 82. Also, \angle QRS = \angle RST = \angle STP = 90^\circ. The area of the pentagon PQRST is

\textbf{(A)}\ 306\quad \textbf{(B)}\ 297\quad \textbf{(C)}\ 288\quad \textbf{(D)}\ 279\quad \textbf{(E)}\ 270

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 Cayley contests here.