Question

The surface area of a square pyramid can be calculated using the equation S = 1/2 lp +B.

Answer 1

The formula you provided for the surface area \( S \) of a square pyramid is correct and can be explained in more detail:

- \( S \) represents the total surface area of the pyramid.
- \( l \) is the slant height of the pyramid.
- \( p \) is the perimeter of the base of the pyramid.
- \( B \) is the area of the base of the pyramid.

For a square pyramid specifically:

1. **Base Area (\( B \))**: If the length of one side of the square base is \( a \), then the area of the base is:
\[
B = a^2
\]

2. **Perimeter (\( p \))**: The perimeter of the square base is:
\[
p = 4a
\]

3. **Surface Area Formula**: Plugging these into the surface area equation, we can express the complete formula as:
\[
S = \frac{1}{2} l(4a) + a^2
\]
This simplifies to:
\[
S = 2la + a^2
\]

So, the total surface area of a square pyramid can ultimately be calculated using the equation:
\[
S = 2la + a^2
\]
If you know the side length of the base and the slant height, you can easily calculate the surface area of a square pyramid.