Which formula correctly gives the surface area of a prism with base perimeter P, base area B, and height h?

Which formula correctly gives the surface area of a prism with base perimeter P, base area B, and height h?

• A. SA = (Base-Perimeter) h + 2(Base-Area)
• B. SA = Base-Perimeter h
• C. SA = 2Base-Area + Base-Perimeter
• D. SA = 2(Base-Perimeter)h + Base-Area

Answer: (A)

The surface area of a prism comes from adding the areas of the two bases and the rectangular side faces. The two bases contribute twice the base area, which is 2B. The side faces form rectangles whose combined area equals the base perimeter times the height, which is P times h. So the total surface area is 2B + P h. The given formula (Base-Perimeter) h + 2(Base-Area) is Ph + 2B, which matches exactly. This is why that choice is correct.

The surface area of a prism comes from adding the areas of the two bases and the rectangular side faces. The two bases contribute twice the base area, which is 2B. The side faces form rectangles whose combined area equals the base perimeter times the height, which is P times h. So the total surface area is 2B + P h. The given formula (Base-Perimeter) h + 2(Base-Area) is Ph + 2B, which matches exactly. This is why that choice is correct.