1. **Problem statement:** We are given two similar equilateral triangles with areas 396 cm² and 275 cm² respectively. 2. **Find the ratio of the areas:** The ratio of the areas is given by $$\frac{396}{275} = \frac{36}{25}$$ 3. **Recall the relationship between side lengths and areas in similar triangles:** If two triangles are similar, the ratio of their areas is the square of the ratio of their corresponding sides. 4. **Calculate the ratio of corresponding sides:** Let the ratio of corresponding sides (large to small) be $\frac{a}{b}$. Then, $$\left(\frac{a}{b}\right)^2 = \frac{36}{25}$$ Taking the square root of both sides, $$\frac{a}{b} = \sqrt{\frac{36}{25}} = \frac{6}{5}$$ 5. **Final answer:** - Ratio of areas: $\frac{36}{25}$ - Ratio of corresponding sides (large to small): $\frac{6}{5}$