1. **Problem statement:** We have a tent shaped as a triangular prism with base triangle sides 2.5 m, 2.5 m, and 1.5 m height, length of prism 6 m, and base of prism 4 m. We need to find total calico needed (surface area), volume of the tent, and cost of calico at 20 per m². 2. **Given dimensions:** - Triangle sides: two equal sides 2.5 m, height 1.5 m, base 4 m (from description, base is horizontal length 4 m) - Prism length (depth): 6 m 3. **i) Show total calico needed (surface area) is 60 m²:** - Triangular faces area (2 faces): Each triangle's area = $$\frac{1}{2} \times base \times height = \frac{1}{2} \times 4 \times 1.5 = 3 \text{ m}^2$$ - Total for two triangular faces = $$2 \times 3 = 6 \text{ m}^2$$ - Rectangular faces (3 faces): - Base rectangle: length of prism $$6\text{ m} \times base 4\text{ m} = 24 \text{ m}^2$$ - Two equal rectangles (sides): Each is $$6\text{ m} \times 2.5 \text{ m} = 15 \text{ m}^2$$ - Both sides together: $$2 \times 15 = 30 \text{ m}^2$$ - Total rectangular area = $$24 + 30 = 54 \text{ m}^2$$ 4. **Sum total surface area:** $$6 + 54 = 60 \text{ m}^2$$ This confirms the total calico needed is 60 m². 5. **ii) Calculate the volume of the tent:** - Volume = base area of triangle \( \times \) length of prism - Base area of triangle = 3 m² (as above) - Length of prism = 6 m - Volume = $$3 \times 6 = 18 \text{ m}^3$$ 6. **Calculate total cost of calico:** - Cost per m² = 20 - Total calico area = 60 m² - Total cost = $$60 \times 20 = 1200$$ **Final answers:** - Total calico needed (surface area) = 60 m² - Volume of the tent = 18 m³ - Total cost of calico material = 1200