1. **Problem statement:** Calculate the scaled dimensions and the front area of a hexagonal house drawn at a scale of 1:200. 2. **Choosing the height:** Architects often choose a floor height between 2m and 2.5m. For this problem, let's select a height of 2.5m for one floor to allow comfortable living space. 3. **Scaling dimensions:** If the real house has length $L$, width $W$, and height $H$, the scaled dimensions $L_s$, $W_s$, and $H_s$ are given by: $$L_s = \frac{L}{200}, \quad W_s = \frac{W}{200}, \quad H_s = \frac{H}{200}$$ 4. **Example dimensions:** Assume the real house has length $L=20m$, width $W=15m$, and height $H=2.5m$ (one floor). 5. **Calculate scaled dimensions:** $$L_s = \frac{20}{200} = 0.1m = 10cm$$ $$W_s = \frac{15}{200} = 0.075m = 7.5cm$$ $$H_s = \frac{2.5}{200} = 0.0125m = 1.25cm$$ 6. **Calculate front area:** The front side is a rectangle with length $L$ and height $H$. $$A = L \times H = 20m \times 2.5m = 50m^2$$ 7. **Scaled front area:** Since area scales with the square of the scale factor: $$A_s = \left(\frac{1}{200}\right)^2 \times A = \frac{1}{40000} \times 50 = 0.00125m^2 = 12.5cm^2$$ **Summary:** - Chosen height: 2.5m - Scaled length: 10cm - Scaled width: 7.5cm - Scaled height: 1.25cm - Front area: 50m² (real), 12.5cm² (scaled) This method can be applied to any given dimensions by substituting the real values into the formulas above.