CAYLEY 2020 Problem 10

In the diagram, pentagon P Q R S T has P Q=13, Q R=18, S T=30, and a perimeter of 82. Also, \angle Q R S=\angle R S T=\angle S T P=90^{\circ}. The area of the pentagon P Q R S T is

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Answer Choices
A. 306
B. 297
C. 288
D. 279
E. 270