Inside the square below, with a side measuring $5 \mathrm{~cm}$, a star was created by drawing four identical isosceles triangles, each measuring $1 \mathrm{~cm}$ in height. Find an irreducible fraction that represents the ratio between the area of the star and the area of the square.

![](https://cdn.mathpix.com/cropped/2024_05_01_ffb48c2069f209c1311cg-13.jpg?height=460&width=430&top_left_y=1034&top_left_x=890)

Note: A triangle is isosceles if two of its sides are equal.
Solution

The area of the square is $5 \cdot 5=25$. The area of each triangle is $\frac{5 \cdot 1}{2}$. Therefore, the area of the star is $25-4 \cdot \frac{5}{2}=15$. Thus, the ratio between the area of the star and the area of the square is $\frac{15}{25}=\frac{3}{5}$.