The flowers of Geometrix have very interesting shapes. Some of them have the form shown in Figure 12.1, where there are six squares and twelve equilateral triangles.

![](https://cdn.mathpix.com/cropped/2024_05_01_4e05cbad380df980abcfg-2.jpg?height=446&width=534&top_left_y=485&top_left_x=932)

Figure 12.1

A bee landed on the highlighted point and walked along the edge of the flower in a clockwise direction until it returned to the starting point. Knowing that the gray region has an area of $24 \mathrm{~cm}^{2}$, what is the distance traveled by the bee?
The highlighted area corresponds to the sum of the areas of six squares. Therefore, each square has an area of $4 \mathrm{~cm}^{2}$ and a side length of $2 \mathrm{~cm}$.

The sides of the squares and the equilateral triangles are all equal. One complete revolution of the bee around the flower corresponds to 24 times the side of the square, that is, $48 \mathrm{~cm}$.