Problem 3. Given an equilateral triangle with an area of $6 \mathrm{~cm}^{2}$. On each of its sides, an equilateral triangle is constructed. Calculate the area of the resulting figure.
Solution. In the construction, above each side of the equilateral triangle, we construct an equilateral triangle with a side of the same length as the side of the triangle, which means we add a new equilateral triangle that has the same area as the original equilateral triangle. Therefore, the resulting figure consists of four equilateral triangles equal to the original equilateral triangle. Thus, the area of the resulting figure is four times larger than the area of the equilateral triangle, i.e., $P=4 \cdot 6=24 \mathrm{~cm}^{2}$.