Question 1: Calculate the surface area of a prism with a rectangular base of length 8 cm, width 3 cm, and height 10 cm, by adding the areas of all its faces.

Answer: 180

Question 2: A triangular prism has a base triangle with sides 5 cm, 6 cm, and 7 cm, and a length of 12 cm. Add the lateral faces to find the total surface area.

Answer: Calculate based on given dimensions

Question 3: A prism's three visible faces are 24 cm², 30 cm², and 18 cm². The prism has two additional faces. If the total surface area is 102 cm², find the combined area of the hidden faces.

Answer: 30

Question 4: Construct a rectangular prism on the grid with a surface area of 94 cm², given that its length is 7 cm, width is 4 cm, and height is unknown. Add faces to verify the total surface area.

Answer: Height = 5 cm

Question 5: A cylindrical container is approximated as a prism with 4 rectangular faces. If the total surface area of this prism is 150 cm², and three faces are 40 cm², 35 cm², and 20 cm², what is the area of the remaining face?

Answer: 55

Question 6: A pentagonal prism has five rectangular faces and two pentagonal bases. If each rectangular face has an area of 15 cm², and the total surface area is 135 cm², how much area is covered by the two bases combined?

Answer: 60

Question 7: A prism has three visible faces with areas 22 cm², 18 cm², and 26 cm². The total surface area is 80 cm². Add the hidden faces' areas and identify any common mistakes students might make.

Answer: 14; common mistake: double-counting faces

Question 8: A composite prism consists of a rectangular prism atop a triangular prism. The rectangular prism has faces totaling 48 cm², and the triangular prism's visible faces total 36 cm². Add all faces to find the total surface area, assuming no shared faces are double-counted.

Answer: 84

Question 9: A prism has a top face of 20 cm² and four lateral faces averaging 25 cm² each. Add the faces to find the total surface area and note the assumptions made about face shapes.

Answer: 120

Question 10: Identify and correct the common mistake: A student claims that to find the total surface area, they simply multiply the perimeter of the base by the height, then add twice the base area.

Answer: Incorrect; this is the lateral surface area, not total surface area.

Question 11: Challenge: A prism's three faces have areas 36, 48, and 54 cm². The total surface area exceeds 150 cm². Find the possible areas of the remaining faces if the prism is an irregular shape, explaining your reasoning.

Answer: Remaining faces sum to at least 54 cm²; reasoning involves considering possible face configurations.