Question

Look at the square pyramid below.



56 mi56\ \text{mi}56 mi lll

33 mi33\ \text{mi}33 mi

How many miles long is the slant height of the square pyramid? Click Here for Help Video.

Answer 1

To calculate the slant height of a square pyramid, we need to use the Pythagorean theorem. The slant height (l) can be found using the formula:

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

where:
- \( h \) is the height of the pyramid (the vertical height from the base to the apex),
- \( b \) is the length of one side of the base.

From your description, we have:
- The height \( h = 33 \, \text{mi} \)
- The length of one side of the base \( b = 56 \, \text{mi} \)

Now, we can perform the calculation:

1. Calculate \( \frac{b}{2} \):
\[
\frac{b}{2} = \frac{56}{2} = 28 \, \text{mi}
\]

2. Now apply the Pythagorean theorem:
\[
l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2} = \sqrt{33^2 + 28^2}
\]

3. Calculate \( 33^2 \):
\[
33^2 = 1089
\]

4. Calculate \( 28^2 \):
\[
28^2 = 784
\]

5. Now add these two results:
\[
1089 + 784 = 1873
\]

6. Finally, take the square root:
\[
l = \sqrt{1873} \approx 43.29 \, \text{mi} \quad (\text{rounded to two decimal places})
\]

So, the slant height of the square pyramid is approximately \( 43.29 \, \text{mi} \).