Question

Apply the Pythagorean theorem to determine the height of the square pyramid, h. Round the answer to the nearest tenth.

Answer 1

To apply the Pythagorean theorem to determine the height \( h \) of a square pyramid, we first need to understand the components involved.

1. **Identify the components**:
- Let \( a \) be the length of a side of the base of the pyramid.
- The height \( h \) is the vertical distance from the apex of the pyramid to the center of the base.
- The slant height \( l \) is the distance from the apex down to the midpoint of one of the edges of the base.

2. **Use the Pythagorean theorem**:
The relationship can be expressed using:
\[
l^2 = h^2 + \left(\frac{a}{2}\right)^2
\]
Where:
- \( l \) is the slant height,
- \( h \) is the height from the apex to the base,
- \( \frac{a}{2} \) is half the side length of the base.

3. **Rearranging for height \( h \)**:
From the equation above, we can rearrange to solve for \( h \):
\[
h^2 = l^2 - \left(\frac{a}{2}\right)^2
\]
\[
h = \sqrt{l^2 - \left(\frac{a}{2}\right)^2}
\]

### Example Calculation
If you provide specific values for \( a \) (the side length of the base) and \( l \) (the slant height), I can calculate the height \( h \) for you.

### Final Steps
1. Plug in the values of \( a \) and \( l \).
2. Calculate the value of \( h \).
3. Round \( h \) to the nearest tenth.

Please provide the values for \( a \) and \( l \) so that I can perform the calculations.