AMC 12 2023b Problem 11

What is the maximum area of an isosceles trapezoid that has legs of length $1$ and one base twice as long as the other?

$\textbf{(A) }\frac 54 \textbf{(B) } \frac 87 \textbf{(C)} \frac{5\sqrt2}4 \textbf{(D) } \frac 32 \textbf{(E) } \frac{3\sqrt3}4$