Mr. Kutil wanted to paint star ornaments on 20 tiles in the bathroom. On the can of paint, it was written that the paint would cover $750 \mathrm{~cm}^{2}$. How many cans of paint did Mr. Kutil have to buy at least, if one square of the grid has an area of $1 \mathrm{~cm}^{2}$? The ornament on one tile is shown in the picture.

(L. Hozová)

![](https://cdn.mathpix.com/cropped/2024_04_17_151e4384192b9f5c88c8g-1.jpg?height=454&width=448&top_left_y=752&top_left_x=838)
The tile is a square with a side of $12 \mathrm{~cm}$, its area is $(12 \mathrm{~cm})^{2}=144 \mathrm{~cm}^{2}$.

Let's calculate the area of the parts that will not be colored:

4 pentagons in the corners have a total area of $4 \cdot 15 \mathrm{~cm}^{2}=60 \mathrm{~cm}^{2}$,

4 isosceles triangles in the middle of the sides have a total area of $4 \cdot \frac{4 \cdot 6}{2} \mathrm{~cm}^{2}=$ $=48 \mathrm{~cm}^{2}$.

The total uncolored area of the tile is $(60+48) \mathrm{~cm}^{2}=108 \mathrm{~cm}^{2}$.

The colored part of the tile has an area of $(144-108) \mathrm{~cm}^{2}=36 \mathrm{~cm}^{2}$.

The colored area of 20 tiles is $(36 \cdot 20) \mathrm{~cm}^{2}=720 \mathrm{~cm}^{2}$,

$$
720 \mathrm{~cm}^{2}<750 \mathrm{~cm}^{2} \quad \text { (1 can). }
$$

Mr. Kutil will have enough with one can of paint to color the ornaments on 20 tiles.