Starting from an equilateral triangle like the one in figure a, trisect each side of the triangle, and then construct new equilateral triangles outward using the middle segments as sides, as shown in figure b, to get a "snowflake hexagon". Next, trisect each of the 12 sides of the "snowflake hexagon" and construct new equilateral triangles outward using the middle segments as sides, as shown in figure c, to get a new "snowflake shape". What is the ratio of the area of figure c to the area of figure a?
17. Answer: $40: 27$

Analysis: Let the area of the equilateral triangle in figure $\mathrm{a}$ be 1. In figure $\mathrm{b}$, the area of each additional equilateral triangle added to each side is $\frac{1}{9}$. A total of 3 equilateral triangles are added, so the ratio of the area of figure $\mathrm{b}$ to the area of figure $\mathrm{a}$ is $\frac{4}{3}$. Similarly, in figure $\mathrm{c}$, the area of the smaller equilateral triangles added to the outer edge is $\frac{1}{9} \times \frac{1}{9}=\frac{1}{81}$. A total of 12 smaller equilateral triangles are added, so the area of figure $\mathrm{c}$ is $\frac{4}{3}+12 \times \frac{1}{81}=\frac{4}{3}+\frac{4}{27}=\frac{40}{27}$. 
Therefore, the ratio of the area of figure $\mathrm{c}$ to the area of figure $\mathrm{a}$ is 40:27.