1. **State the problem:** Florence has a rectangular field 40 m long and 25 m wide. She reduces both length and width by 20%. We need to find the percentage reduction in the area. 2. **Formula for area of a rectangle:** $$\text{Area} = \text{length} \times \text{width}$$ 3. **Calculate original area:** $$\text{Original area} = 40 \times 25 = 1000 \text{ m}^2$$ 4. **Calculate new dimensions after 20% reduction:** Length reduced by 20% means new length is: $$40 - 0.20 \times 40 = 40 \times (1 - 0.20) = 40 \times 0.80 = 32 \text{ m}$$ Width reduced by 20% means new width is: $$25 - 0.20 \times 25 = 25 \times (1 - 0.20) = 25 \times 0.80 = 20 \text{ m}$$ 5. **Calculate new area:** $$\text{New area} = 32 \times 20 = 640 \text{ m}^2$$ 6. **Calculate area reduction:** $$\text{Area reduction} = 1000 - 640 = 360 \text{ m}^2$$ 7. **Calculate percentage reduction in area:** $$\text{Percentage reduction} = \frac{360}{1000} \times 100 = 36\%$$ **Final answer:** The area is reduced by **36%**.