What is the formula for the surface area of a pyramid with base perimeter p, slant height l, and base area b?

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Multiple Choice

What is the formula for the surface area of a pyramid with base perimeter p, slant height l, and base area b?

Explanation:
The surface area of a pyramid comes from adding the area of the base to the area of the sides (the lateral surface). The lateral surface area can be found by summing the areas of the triangular faces. Each triangular face has area (1/2) times its base edge length and the slant height, and when you sum over all base edges, you get (1/2) times the base perimeter p times the slant height l. So the total surface area is base area plus lateral area: SA = b + (1/2) p l, which can be written as (1/2) p l + b. Height is used for volume, not surface area, so an expression that adds height would not be correct for surface area.

The surface area of a pyramid comes from adding the area of the base to the area of the sides (the lateral surface). The lateral surface area can be found by summing the areas of the triangular faces. Each triangular face has area (1/2) times its base edge length and the slant height, and when you sum over all base edges, you get (1/2) times the base perimeter p times the slant height l. So the total surface area is base area plus lateral area: SA = b + (1/2) p l, which can be written as (1/2) p l + b.

Height is used for volume, not surface area, so an expression that adds height would not be correct for surface area.

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