What formula is used to calculate the lateral area of a pyramid?

To determine the lateral area of a pyramid, the correct formula involves the perimeter of the base and the height from the base to the apex, specifically the slant height of the pyramid. The lateral area can be derived by calculating the area of the triangular faces that connect the base to the apex.

The formula used to calculate the lateral area of a pyramid is indeed half of the perimeter of the base times the slant height. This approach works because each triangular face's area can be calculated as (1/2 * base * height), where the base corresponds to a side of the pyramid's base and the height is the slant height of that face.

Using the base's perimeter allows the calculation to encompass all triangular sides of the pyramid, which is why taking half the perimeter times the slant height accurately reflects the total lateral area. Each triangular side contributes to the total, thereby justifying why this formula is the appropriate choice. Thus, the formula accurately represents the geometric principles underlying pyramids and their lateral surface calculations.