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?

A. $1 : 3$

B. $3 : 8$

C. $5 : 12$

D. $7 : 16$

E. $4 : 9$