7.2. Cut a $5 \times 6$ grid rectangle along the grid lines into five figures, the areas of which will be five consecutive natural numbers, and the perimeter of each figure will be twice its area.
Solution. Let's find the areas of the required polygons. Let $x$ be the area of the polygon with the smallest area. Then $x + x + 1 + x + 2 + x + 3 + x + 4 = 30$, from which $x = 4$, so the areas of the polygons are $4, 5, 6, 7, 8$. Then their perimeters are $8, 10, 12, 14$, and 16, respectively. The figure below shows an example of a possible cutting.

Remark. It is sufficient for the participant to provide any correct example of cutting, without explaining how it was obtained. In turn, during verification, it is necessary to ensure that all conditions are met. The perimeters of the polygons can be controlled by mentally "inscribing" the grid polygon in a rectangle with the same perimeter: $8 - 2 \times 2, 10 - 2 \times 3, 12 - 2 \times 4, 14 - 3 \times 4, 16 - 2 \times 6$.

![](https://cdn.mathpix.com/cropped/2024_05_06_16d1e9b9e4230ee9f955g-1.jpg?height=414&width=310&top_left_y=2240&top_left_x=1658)

Comment. A correct example is given - 7 points. A correct drawing is sufficient justification for the answer, and points should not be deducted for the lack of explanations.