In the image, there are two white squares in a gray field. The sides of the image and the sides of both squares are oriented horizontally or vertically:

![](https://cdn.mathpix.com/cropped/2024_04_17_4fa64f00d3e913cb7404g-2.jpg?height=514&width=531&top_left_y=1793&top_left_x=768)

The dotted distances from the sides of the smaller square to the sides of the image are the same as the side length of this square. The dashed distances from the sides of the larger square to the sides of the image are the same as the side length of this square. The area of the gray part of the image is $62 \mathrm{~cm}^{2}$.

Determine the area of the white part of the image. (E. Semerádová)
The size of the (left horizontal) dashed line segment is the same as the sum of the sizes of the dotted line segment and the side of the smaller square. Therefore, the size of the dashed line segment is double the size of the dotted line segment relative to $\mathrm{k}$, or the side of the larger square is double the side of the smaller square. The entire figure can thus be divided into fields identical to the smaller white square:

![](https://cdn.mathpix.com/cropped/2024_04_17_4fa64f00d3e913cb7404g-3.jpg?height=525&width=546&top_left_y=577&top_left_x=755)

The larger white square is composed of 4 fields. There are a total of 5 white fields $(1+4=5)$. There are 36 fields in total $(6 \cdot 6=36)$. There are 31 gray fields $(36-5=31)$.

The gray part has an area of $62 \mathrm{~cm}^{2}$, so the area of one field is $2 \mathrm{~cm}^{2} (62: 31=2)$. There are 5 white fields, so the white part of the image has an area of $10 \mathrm{~cm}^{2} (5 \cdot 2=10)$.

Evaluation: 1 point for recognizing the ratio of the sides of the white squares; 1 point for dividing the figure and counting the white and gray fields; 2 points for the area of one field; 2 points for the area of the white part of the image.