Question 1: Calculate the total area of the three visible faces of a triangular prism with a rectangular base of length 8 cm, height 5 cm, and a triangular face with base 8 cm and height 6 cm.

Answer: 78

Question 2: A rectangular prism has length 10 cm, width 4 cm, and height 7 cm. If the top and front faces are removed, what is the total area of the remaining visible faces?

Answer: 290

Question 3: Construct a rectangular prism on the grid with dimensions: length 6 cm, width 3 cm, height 4 cm. Then, add the areas of all its faces.

Answer: 108

Question 4: A cylindrical container with height 12 cm and diameter 6 cm is cut along its length. The lateral surface is flattened. How much face area is added when the side is unwrapped and the two circular ends are added?

Answer: 144

Question 5: A rectangular-based prism has dimensions 5 cm by 7 cm by 3 cm. Calculate the total surface area by adding all the faces.

Answer: 94

Question 6: A cube has side length 4 cm. What is the total area of all its faces combined? Show your working.

Answer: 96

Question 7: Explain how adding the areas of the faces of a prism helps determine its surface area. Use a rectangular prism as an example.

Answer: By summing the areas of all individual faces, we find the total surface area. For example, a rectangular prism's surface area includes two rectangles for the top and bottom, and four rectangles for the sides. Adding these gives the total surface area.

Question 8: A triangular prism has a rectangular base of 8 cm, height 6 cm, and a length (depth) of 10 cm. The two triangular faces are identical. Calculate the combined area of the three visible faces (one rectangle and two triangles).

Answer: 124

Question 9: A box-shaped container is 15 cm long, 9 cm wide, and 4 cm high. If the container is filled with a liquid and the lid is removed, what is the total area of the six faces? Show your calculations.

Answer: 354

Question 10: Identify and correct the mistake in this student solution: 'Surface area of a rectangular prism with length 8 cm, width 3 cm, height 5 cm is calculated as 2×(8×3 + 8×5 + 3×5) = 94 cm². The correct total should be 94 cm², so the calculation is right.'

Answer: The calculation is correct; no mistake.

Question 11: Challenge: A trapezoidal prism has a rectangular base 6 cm by 4 cm, with the trapezoidal faces having bases of 6 cm and 8 cm, and height 3 cm. The length of the prism is 10 cm. Calculate the total area of all faces by adding faces appropriately.

Answer: 172