*Author's Note*: I got this puzzle from Nicolay Tchernitsky.

Examine the drawing in Figure 1.

**Figure 1: **Equilateral Triangles Puzzle

The triangle ABC is an equilateral triangle with an area S and a side length a. The line CF is a continuation of the line AC, AD is a continuation of BA and BE is a continuation of CB. The length of all continuation segments (CF, AD and BE) is a—the same as the length of triangle ABC’s sides. **The puzzle is to calculate the area of the triangle DEF.**

Cheers,

BG