1. **State the problem:** We need to find how many tiles are required to cover a stepped polygon wall with given dimensions, then calculate the total cost including tile price, labor, and VAT. 2. **Calculate the area of the wall:** The wall is a stepped polygon with three horizontal segments on top: 70 cm, 60 cm, and 70 cm, and vertical heights of 90 cm on the left and 75 cm on the right, with a total bottom length of 200 cm. 3. **Divide the wall into two rectangles:** - Left rectangle: width = 70 cm + 60 cm = 130 cm, height = 90 cm - Right rectangle: width = 70 cm, height = 75 cm 4. **Calculate areas:** $$\text{Area}_{left} = 130 \times 90 = 11700 \text{ cm}^2$$ $$\text{Area}_{right} = 70 \times 75 = 5250 \text{ cm}^2$$ 5. **Total area:** $$\text{Area}_{total} = 11700 + 5250 = 16950 \text{ cm}^2$$ 6. **Convert area to square meters:** $$16950 \text{ cm}^2 = \frac{16950}{10000} = 1.695 \text{ m}^2$$ 7. **Calculate number of tiles:** Assuming each tile is 1 dm² (10 cm x 10 cm = 100 cm²), number of tiles needed: $$\frac{16950}{100} = 169.5 \approx 170 \text{ tiles}$$ 8. **Calculate cost of tiles:** $$170 \times 2.50 = 425$$ 9. **Calculate labor cost:** Labor charges €50 per 0.5 m², so for 1.695 m²: $$\frac{1.695}{0.5} = 3.39 \text{ units}$$ Labor cost: $$3.39 \times 50 = 169.5$$ 10. **Calculate total before VAT:** $$425 + 169.5 = 594.5$$ 11. **Add VAT at 21%:** $$594.5 \times 1.21 = 719.745$$ 12. **Round to nearest euro:** $$720$$ **Final answers:** - Number of tiles needed: **170** - Total cost including VAT: **720** euros