Use the table to answer the question.

Question

A table describing the steps to finding the formula for the surface area of a square pyramid is partially filled in below.

Step and Description Formulas
1. Area of the square base 1.
2. Area of one triangular side 2.
3. Combined area for all four triangles 3.
4. Surface area formula 4.




Which formula corresponds to step 3?

(1 point)
Responses

12sl
1 half s l

2sh
2 s h

2sl

Answer 1

To find the total combined area of all four triangular sides of a square pyramid, we need to consider the area of one triangular side and then multiply that by four.

1. The area of one triangular side can be expressed as \( \frac{1}{2} \times \text{base} \times \text{height} \). In the case of a square pyramid, the base of the triangular side is a side of the square base (denoted as \( s \)) and the height of the triangular side (from the base to the apex of the pyramid) is denoted as \( l \). Therefore, the area of one triangular side is \( \frac{1}{2}sl \).

2. To find the combined area for all four triangular sides, we multiply the area of one triangular side by 4. This gives us: \[ 4 \times \frac{1}{2}sl = 2sl \]

Thus, the formula that corresponds to step 3 is 2sl.