Question

Look at the square pyramid below.



55 mi55\ \text{mi}55 mi 𝑙ll

48 mi48\ \text{mi}48 mi

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

Answer 1

To find the slant height of a square pyramid, we can use the Pythagorean theorem. The slant height (\(l\)) forms a right triangle with the height of the pyramid (\(h\)) and half the length of the base (\(\frac{b}{2}\)).

In your case, the base length (\(b\)) is 55 miles, and the height (\(h\)) is 48 miles.

1. First, calculate half the base length:
\[
\frac{b}{2} = \frac{55}{2} = 27.5 \text{ miles}
\]

2. Now, apply the Pythagorean theorem:
\[
l^2 = h^2 + \left(\frac{b}{2}\right)^2
\]
Substituting the height and half the base:
\[
l^2 = 48^2 + 27.5^2
\]
Calculate the squares:
\[
48^2 = 2304
\]
\[
27.5^2 = 756.25
\]
Now, add these values:
\[
l^2 = 2304 + 756.25 = 3060.25
\]

3. Finally, take the square root to find the slant height:
\[
l = \sqrt{3060.25} \approx 55.4 \text{ miles}
\]

Thus, the slant height of the square pyramid is approximately 55.4 miles.