Question

How many miles long is the slant height of the square pyramid?
if the boutom is 33 and one of the sides are 56

Answer 1

To find the slant height of a square pyramid, we can use the Pythagorean theorem. The slant height (\(l\)) is the hypotenuse of a right triangle where one leg is half the length of the base (\(a\)) and the other leg is the height (\(h\)) of the pyramid.

From your question, it seems there might be a small misunderstanding in the dimensions provided. It appears that:
- The "bottom" (base) of the pyramid is \(33\) (which we'll assume is the length of one side of the square base).
- The "one of the sides" (\(56\)) typically would refer to the height of the pyramid.

### Given:
- Base side length, \(a = 33\)
- Height of the pyramid, \(h = 56\)

### Steps to find slant height (\(l\)):
1. Calculate half the base side length:
\[
\frac{a}{2} = \frac{33}{2} = 16.5
\]

2. Use the Pythagorean theorem to find the slant height (\(l\)):
\[
l = \sqrt{h^2 + \left(\frac{a}{2}\right)^2}
\]
Substitute the values into the equation:
\[
l = \sqrt{56^2 + (16.5)^2}
\]
Calculate the squares:
\[
l = \sqrt{3136 + 272.25}
\]
\[
l = \sqrt{3408.25}
\]
Finally, calculate the square root:
\[
l \approx 58.4
\]

### Conclusion:
The slant height of the square pyramid is approximately **58.4 miles**.