124. The side of an equilateral triangle is twice the side of a regular hexagon. Find the ratio of the areas of these two figures.
124. Let the side of a regular hexagon be $a$. Obviously, a regular hexagon consists of six equilateral triangles with side $a$, and a regular triangle - of four (see Fig. 21 and 22). Thus, the ratio of the area of a regular triangle to the area of a regular hexagon is $\frac{4}{6}=\frac{2}{3}$.

![](https://cdn.mathpix.com/cropped/2024_05_21_a21e90374409a05a4ea7g-27.jpg?height=457&width=551&top_left_y=774&top_left_x=524)

Fig. 21

![](https://cdn.mathpix.com/cropped/2024_05_21_a21e90374409a05a4ea7g-27.jpg?height=457&width=529&top_left_y=771&top_left_x=1209)

Fig. 22