1. **State the problem:** We have a piece of land with length 10 meters and width 5 meters. We want to find 90% of the total area of this land to be used for building a house. 2. **Formula for area of a rectangle:** $$\text{Area} = \text{length} \times \text{width}$$ 3. **Calculate the total area:** $$\text{Area} = 10 \times 5 = 50 \text{ square meters}$$ 4. **Find 90% of the total area:** $$90\% = \frac{90}{100} = 0.9$$ 5. **Calculate the area for the house:** $$\text{House area} = 0.9 \times 50 = 45 \text{ square meters}$$ **Final answer:** The area used for building the house is **45 square meters**.