1. **State the problem:** We have a scale of 1 : 500, meaning 1 unit on the drawing represents 500 units in reality. 2. **Given:** Actual area = 125,000 m². We want to find the area on the drawing in cm². 3. **Understand the scale:** Since the scale is linear, the ratio of lengths is $\frac{1}{500}$. 4. **Area scale factor:** Area scales as the square of the length scale, so area scale factor = $\left(\frac{1}{500}\right)^2 = \frac{1}{500^2} = \frac{1}{250000}$. 5. **Calculate the area on the drawing in m²:** $$\text{Area on drawing (m}^2) = 125000 \times \frac{1}{250000} = \frac{125000}{250000} = \frac{1}{2} = 0.5\, \text{m}^2$$ 6. **Convert m² to cm²:** Since $1\, \text{m} = 100\, \text{cm}$, then $$1\, \text{m}^2 = (100\, \text{cm})^2 = 10000\, \text{cm}^2$$ 7. **Final area on drawing in cm²:** $$0.5\, \text{m}^2 = 0.5 \times 10000 = 5000\, \text{cm}^2$$ **Answer:** The area of the field on the drawing is $5000\, \text{cm}^2$.