1. **Problem:** Two similar triangles have the ratio of their corresponding sides as 3:4. Find the ratio of their areas. 2. **Formula and Rules:** - The ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides. - If the side ratio is $\frac{a}{b}$, then the area ratio is $\left(\frac{a}{b}\right)^2$. 3. **Work:** - Given side ratio = $\frac{3}{4}$ - Area ratio = $\left(\frac{3}{4}\right)^2 = \frac{9}{16}$ 4. **Explanation:** - Since the triangles are similar, their areas scale by the square of the scale factor of their sides. - So, the area of the smaller triangle to the larger triangle is $9:16$. **Final answer:** The ratio of their areas is $9:16$.