Which expression gives the surface area of a prism with base perimeter P and base area B?

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Multiple Choice

Which expression gives the surface area of a prism with base perimeter P and base area B?

Explanation:
The surface area of a prism comes from adding the lateral surface area to the areas of the two bases. The sides around the prism, when unwrapped, form a rectangle with height equal to the prism’s height and width equal to the base perimeter, so the lateral area is the base perimeter times the height (P and h). The two bases each have area B, so together they add 2B. Put together: surface area = Ph + 2B. This matches the given expression. The other forms don’t align with this combination of lateral area and two bases.

The surface area of a prism comes from adding the lateral surface area to the areas of the two bases. The sides around the prism, when unwrapped, form a rectangle with height equal to the prism’s height and width equal to the base perimeter, so the lateral area is the base perimeter times the height (P and h). The two bases each have area B, so together they add 2B. Put together: surface area = Ph + 2B. This matches the given expression. The other forms don’t align with this combination of lateral area and two bases.

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