Tam created the mosaic shown using a regular hexagon, squares and equilateral triangles. If the side length of the hexagon is $20 \mathrm{~cm}$, what is the outside perimeter of the mosaic?

![](https://cdn.mathpix.com/cropped/2024_04_17_d0cbae19e125c7a52478g-1.jpg?height=312&width=325&top_left_y=1530&top_left_x=954)
Since each square shares a side with the hexagon, the side lengths of the squares are $20 \mathrm{~cm}$.

Since each equilateral triangle shares a side with a square (in fact, with two squares), the side lengths of the triangles are $20 \mathrm{~cm}$.

The perimeter of the mosaic is made up of one side from each of the six squares and one side from each of the six triangles.

Therefore, the perimeter of the mosaic is $12 \times 20 \mathrm{~cm}=240 \mathrm{~cm}$.

ANSWER: $240 \mathrm{~cm}$