Question

How many miles long is the slant height of the square pyramid?
The left side is 56 mi.The bottme is 33mi and the left side is I.

Answer 1

To find the slant height of a square pyramid, we need to understand the dimensions provided. In your case, it seems there might be some confusion in the description of the sides.

Let’s clarify the dimensions:

- If "the left side" refers to the height of the pyramid, we denote this as \( h = 56 \) mi.
- The base of the pyramid is square, with each side being \( b = 33 \) mi.

To find the slant height (\( l \)) of the pyramid, we can use the following relationship:

1. The slant height is the distance from the midpoint of one of the base edges to the apex (the top of the pyramid).
2. This forms a right triangle where:
- One leg is half the length of the base, \( \frac{b}{2} = \frac{33}{2} = 16.5 \) mi.
- The other leg is the height of the pyramid, \( h = 56 \) mi.

Now we can apply the Pythagorean theorem:

\[
l^2 = \left(\frac{b}{2}\right)^2 + h^2
\]

Substituting the values:

\[
l^2 = (16.5)^2 + (56)^2
\]
\[
l^2 = 272.25 + 3136
\]
\[
l^2 = 3408.25
\]

Now, take the square root to find \( l \):

\[
l = \sqrt{3408.25} \approx 58.4 \text{ mi}
\]

Thus, the slant height of the square pyramid is approximately **58.4 miles**.