In a square grid, points $A$ to $H$ are marked. The area of square $A B C D$ is $72 \mathrm{~cm}^{2}$.

Determine the area of the star $A E B F C G D H$.

(K. Pazourek)

![](https://cdn.mathpix.com/cropped/2024_04_17_4838e41583d9242a8d6cg-2.jpg?height=777&width=786&top_left_y=454&top_left_x=635)
The entire figure can be divided into four congruent parts by the lines $A C$ and $B D$ (their common point is denoted as $S$). In each part, the area of the portion belonging to the square is three times the area of the portion belonging to the star (for example, the triangles $A S B$ and $E S B$).

The area of the entire star is therefore one-third of the area of the entire square, which we know. The area of the star is $72: 3=24\left(\mathrm{~cm}^{2}\right)$.

Note. From the problem statement, the area (or dimensions) of the smallest squares in the grid can be derived, and then the area of the star: The area of the square corresponds to the area of 18 grid squares; the area of a grid square is $72: 18=4\left(\mathrm{~cm}^{2}\right)$. The area of the star corresponds to the area of 6 grid squares; the area of the star is $6 \cdot 4=24\left(\mathrm{~cm}^{2}\right)$.

Evaluation. 3 points for partial insights; 3 points for the conclusion and quality of the commentary.