1. **Problem statement:** If the side length of a square is increased four times, find the percent increase in the area of the square. 2. **Formula for area of a square:** The area $A$ of a square with side length $s$ is given by $$A = s^2$$ 3. **Initial area:** Let the original side length be $s$. Then the original area is $$A_1 = s^2$$ 4. **New side length:** The side length is increased four times, so the new side length is $$4s$$ 5. **New area:** The new area is $$A_2 = (4s)^2 = 16s^2$$ 6. **Calculate the increase in area:** $$\text{Increase} = A_2 - A_1 = 16s^2 - s^2 = 15s^2$$ 7. **Percent increase:** The percent increase is given by $$\frac{\text{Increase}}{A_1} \times 100 = \frac{15s^2}{s^2} \times 100 = 15 \times 100 = 1500\%$$ **Final answer:** The area increases by 1500%.