1. **State the problem:** We have a tent shaped as a triangular prism with triangular faces of sides 2.5 m, 2.5 m, and 4 m. The height of the triangle is 1.5 m, and the length (depth) of the prism is 6 m. We need to find: - i) The total surface area (calico needed). - ii) The volume of the tent. --- 2. **Calculate the area of one triangular face:** The formula for the area of a triangle is: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ Given base $=4$ m and height $=1.5$ m: $$\text{Area} = \frac{1}{2} \times 4 \times 1.5 = 2 \times 1.5 = 3 \text{ m}^2$$ --- 3. **Calculate the total area of the two triangular faces:** $$2 \times 3 = 6 \text{ m}^2$$ --- 4. **Calculate the area of the three rectangular faces:** The prism sides correspond to the three sides of the triangle multiplied by the length (depth) of the prism 6 m. Each rectangular face area: - Side 1: $2.5 \times 6 = 15$ m² - Side 2: $2.5 \times 6 = 15$ m² - Side 3: $4 \times 6 = 24$ m² Sum of the three rectangular faces: $$15 + 15 + 24 = 54 \text{ m}^2$$ --- 5. **Calculate total surface area of the triangular prism:** $$\text{Total Surface Area} = \text{Area of 2 triangular faces} + \text{Area of 3 rectangular faces} = 6 + 54 = 60 \text{ m}^2$$ So, total calico needed is $60$ m². --- 6. **Calculate the volume of the tent:** Volume of a prism = area of the base × length Area of base (triangle) $= 3$ m², length $=6$ m $$\text{Volume} = 3 \times 6 = 18 \text{ m}^3$$ --- **Final answers:** - Surface Area = $60$ m² - Volume = $18$ m³