Answer: E

Small Hint:

Two pentagon sides are the original rectangle’s full side lengths

Big Hint:

Look for two differences among the lengths that form the legs of a right triangle with a third listed length

Solution:

The full rectangle sides must be longer than the two remnants on those same sides. The only assignment whose two differences and remaining cut side form a right triangle is the rectangle $25$ by $31,$ with remnants $20$ and $19.$ The removed corner then has legs $25-20=5$ and $31-19=12,$ whose hypotenuse is the listed side $13.$ Thus the pentagon’s area is $$\begin{aligned} 25\cdot31-\frac12(5)(12) &=775-30\\ &=745. \end{aligned}$$ Hence the correct answer is E.