2023 AMC 12B 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)} \dfrac{5}{4} \qquad \textbf{(B)} \dfrac{8}{7} \qquad \textbf{(C)} \dfrac{5\sqrt{2}}{4} \qquad \textbf{(D)} \dfrac{3}{2} \qquad \textbf{(E)} \dfrac{3\sqrt{3}}{4}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.