To find the height \( h \) of a square pyramid using the Pythagorean Theorem, we first need to identify the relationships between the height, the base, and the slant height of the pyramid.
Assuming we have a square base of side length \( a \) and the slant height \( s \), we can form a right triangle where:
- One leg is the height \( h \) of the pyramid.
- The other leg is half the length of the base \( \frac{a}{2} \).
- The hypotenuse is the slant height \( s \).
According to the Pythagorean Theorem: \[ s^2 = h^2 + \left(\frac{a}{2}\right)^2 \]
We can rearrange this to find the height \( h \): \[ h^2 = s^2 - \left(\frac{a}{2}\right)^2 \] \[ h = \sqrt{s^2 - \left(\frac{a}{2}\right)^2} \]
Please provide the base length \( a \) and the slant height \( s \) so we can compute the height \( h \).
1 answer