2023 AMC 8 Problem 19

An equilateral triangle is placed inside a larger equilateral triangle so that the region between them can be divided into three congruent trapezoids, as shown below. The side length of the inner triangle is \frac{2}{3} the side length of the larger triangle. What is the ratio of the area of one trapezoid to the area of the inner triangle?

\textbf{(A)} 1 : 3 \qquad \textbf{(B)} 3 : 8 \qquad \textbf{(C)} 5 : 12 \qquad \textbf{(D)} 7 : 16 \qquad \textbf{(E)} 4 : 9

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