1. **State the problem:** We need to find the total surface area of a triangular prism tent, including the floor, to determine how much material Dmitri's mom will need. 2. **Identify the shape and given dimensions:** The tent is a triangular prism with: - Triangular base with sides 1 m, 1 m, and 2 m. - Height of the triangle (perpendicular from base to top vertex) is 1.7 m. - The prism has three rectangular faces with dimensions 2 m by 3 m. 3. **Calculate the area of the triangular base:** The triangle is isosceles with two sides 1 m and base 2 m. The height is given as 1.7 m. Area of triangle = $$\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 1.7 = 1.7$$ square meters. 4. **Calculate the perimeter of the triangular base:** Perimeter = 1 + 1 + 2 = 4 meters. 5. **Calculate the lateral surface area (rectangular faces):** Each rectangle has height 3 m (length of prism) and width equal to a side of the triangle. Total lateral area = perimeter of base $\times$ length = $$4 \times 3 = 12$$ square meters. 6. **Calculate the total surface area:** Total surface area = lateral area + 2 \times area of triangular base (top and floor) = $$12 + 2 \times 1.7 = 12 + 3.4 = 15.4$$ square meters. 7. **Answer:** Dmitri's mom will need exactly $$15.4$$ square meters of material for the tent, including the floor.