1. **Problem 1: Square Box Area Increase** Jordan's wooden box is a square with side length 6 cm. He increases each side by 1.6 cm. 2. **Formula:** Area of a square is $A = s^2$ where $s$ is the side length. 3. **Calculate new side length:** $$6 + 1.6 = 7.6 \text{ cm}$$ 4. **Calculate new area:** $$7.6^2 = 57.76 \text{ cm}^2$$ 5. The problem shows multiplying original area by $1.6^2 = 2.56$: Original area = $6^2 = 36$ cm² New area = $36 \times 2.56 = 92.16$ cm² (rounded to 92.2 cm²) 6. The discrepancy arises because increasing side by 1.6 cm is not the same as scaling by 1.6. The problem's method assumes scale factor 1.6. --- 7. **Problem 2: Triangle Area Scale** Olivia enlarges a triangle with original area 28 using scale factor 1.2. 8. **Formula:** Area scales by the square of the scale factor: $$A_{new} = A_{original} \times (scale\ factor)^2$$ 9. Calculate: $$28 \times 1.2^2 = 28 \times 1.44 = 40.32$$ Rounded to 40.3. --- 10. **Problem 3: Rectangular Cake Area Increase** Original cake dimensions: length 8 cm, width 6 cm. Cream increased by 2 cm around means adding 4 cm total to each dimension. 11. New dimensions: $$8 + 4 = 12 \text{ cm}$$ $$6 + 4 = 10 \text{ cm}$$ 12. New area: $$12 \times 10 = 120 \text{ cm}^2$$ 13. The problem states $4 \times 48 = 192$, which seems to be a different calculation possibly for cream area only. --- 14. **Problem 4: Rectangular Board Area Increase** Original board: length 16 cm, width 10 cm. Increase border by 2 cm around means add 4 cm total to each dimension. 15. New dimensions: $$16 + 4 = 20 \text{ cm}$$ $$10 + 4 = 14 \text{ cm}$$ 16. New area: $$20 \times 14 = 280 \text{ cm}^2$$ --- **Summary:** - For scale factor $k$, area scales by $k^2$. - Increasing each side by a fixed length adds twice that length to each dimension. - Always square the scale factor to find new area.