5. Determine the area of a square with the same perimeter as a regular hexagon with an area of $96 \sqrt{3} \mathrm{~cm}^{2}$.

Problems worth 10 points:
5. A regular hexagon can be divided into 6 equilateral triangles with side length $a$ and height calculated using the Pythagorean theorem $\frac{a \sqrt{3}}{2}$.

$$
\begin{aligned}
& 96 \sqrt{3}=6 \cdot \frac{1}{2} a \cdot \frac{a \sqrt{3}}{2}=\frac{3 a^{2} \sqrt{3}}{2} \\
& 192=3 a^{2} \Rightarrow a^{2}=64 \Rightarrow a=8
\end{aligned}
$$

Perimeter of the hexagon $48 \mathrm{~cm} \Rightarrow$ side length of the square $12 \mathrm{~cm} \Rightarrow$ area of the square $144 \mathrm{~cm}^{2}$