Question
Find the slant height of the square pyramid. Round to the nearest whole inch, if necessary. Show your work.(1 point) 12 and 18
Answers
GPT-4o mini
To find the slant height of a square pyramid, we can use the Pythagorean theorem. In a square pyramid, the slant height (l) can be determined by considering a right triangle formed by half the length of the base (a) and the height (h) of the pyramid.
1. **Identify the base and height:**
- The base is square, so if its side length is given as \( s = 12 \) inches, then:
- **Half of the base length (a)**: \( a = \frac{s}{2} = \frac{12}{2} = 6 \) inches
- The height of the pyramid (h) is given as \( h = 18 \) inches.
2. **Use the Pythagorean theorem:**
The slant height (l) can be calculated using the formula:
\[
l = \sqrt{a^2 + h^2}
\]
3. **Calculate \( l \):**
\[
l = \sqrt{(6)^2 + (18)^2} = \sqrt{36 + 324} = \sqrt{360}
\]
\[
l \approx 18.97
\]
4. **Round to the nearest whole inch:**
\[
l \approx 19 \text{ inches}
\]
Thus, the slant height of the square pyramid is approximately **19 inches**.
1. **Identify the base and height:**
- The base is square, so if its side length is given as \( s = 12 \) inches, then:
- **Half of the base length (a)**: \( a = \frac{s}{2} = \frac{12}{2} = 6 \) inches
- The height of the pyramid (h) is given as \( h = 18 \) inches.
2. **Use the Pythagorean theorem:**
The slant height (l) can be calculated using the formula:
\[
l = \sqrt{a^2 + h^2}
\]
3. **Calculate \( l \):**
\[
l = \sqrt{(6)^2 + (18)^2} = \sqrt{36 + 324} = \sqrt{360}
\]
\[
l \approx 18.97
\]
4. **Round to the nearest whole inch:**
\[
l \approx 19 \text{ inches}
\]
Thus, the slant height of the square pyramid is approximately **19 inches**.