1. Problem statement: Calculate the volume and surface area of a prism with a triangular base with sides 3 cm, 4 cm, 5 cm and height 5 cm. 2. Formula for volume of a prism: $$V = A_{base} \times h$$ where $A_{base}$ is the area of the base and $h$ is the height. 3. Formula for surface area of a prism: $$S = 2 \times A_{base} + A_{mantle}$$ where $A_{mantle}$ is the lateral surface area. 4. Calculate the base area using Heron's formula for a triangle with sides $a=3$, $b=4$, $c=5$: $$s = \frac{a+b+c}{2} = \frac{3+4+5}{2} = 6$$ $$A_{base} = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{6(6-3)(6-4)(6-5)} = \sqrt{6 \times 3 \times 2 \times 1} = \sqrt{36} = 6$$ 5. Calculate volume: $$V = A_{base} \times h = 6 \times 5 = 30$$ cubic cm 6. Calculate lateral surface area (mantle): The perimeter of the base is $P = 3 + 4 + 5 = 12$ $$A_{mantle} = P \times h = 12 \times 5 = 60$$ 7. Calculate total surface area: $$S = 2 \times A_{base} + A_{mantle} = 2 \times 6 + 60 = 12 + 60 = 72$$ square cm 8. Draw the net of the prism: The net consists of the triangular base and top (both congruent triangles) and three rectangles corresponding to the sides 3, 4, and 5 cm each with height 5 cm. Final answers: - Volume: $30$ cubic cm - Surface area: $72$ square cm