1. **State the problem:** We have two similar pentagons, A and B. Pentagon A has a base length of 6.4 cm and an area of 97.6 cm². Pentagon B has a base length of 12.8 cm. We need to find the area of pentagon B. 2. **Recall the formula for areas of similar shapes:** If two shapes are similar, the ratio of their areas is the square of the ratio of their corresponding side lengths. Mathematically, if $\frac{\text{side}_B}{\text{side}_A} = k$, then $$\frac{\text{Area}_B}{\text{Area}_A} = k^2$$ 3. **Calculate the scale factor $k$:** $$k = \frac{12.8}{6.4} = 2$$ 4. **Use the area ratio formula:** $$\frac{\text{Area}_B}{97.6} = 2^2 = 4$$ 5. **Solve for $\text{Area}_B$:** $$\text{Area}_B = 97.6 \times 4 = 390.4$$ **Final answer:** The area of pentagon B is **390.4 cm²**.