Question
Find the slant height of the square pyramid. (1 point) units Skip to navigation From top to bottom is 15 and the base lines are 16
Answers
GPT-4o mini
To find the slant height of a square pyramid, you can use the Pythagorean theorem. The slant height (\( l \)) forms a right triangle with half of the base length and the height (\( h \)) of the pyramid.
In this case:
- The height (\( h \)) of the pyramid is 15 units.
- The base length of the square pyramid is 16 units.
First, find half of the base length:
\[
\text{Half of the base length} = \frac{16}{2} = 8 \text{ units}
\]
Now, use the Pythagorean theorem to calculate the slant height (\( l \)):
\[
l = \sqrt{h^2 + \left(\frac{\text{base length}}{2}\right)^2}
\]
Substituting the values:
\[
l = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289} = 17 \text{ units}
\]
Therefore, the slant height of the square pyramid is **17 units**.
In this case:
- The height (\( h \)) of the pyramid is 15 units.
- The base length of the square pyramid is 16 units.
First, find half of the base length:
\[
\text{Half of the base length} = \frac{16}{2} = 8 \text{ units}
\]
Now, use the Pythagorean theorem to calculate the slant height (\( l \)):
\[
l = \sqrt{h^2 + \left(\frac{\text{base length}}{2}\right)^2}
\]
Substituting the values:
\[
l = \sqrt{15^2 + 8^2} = \sqrt{225 + 64} = \sqrt{289} = 17 \text{ units}
\]
Therefore, the slant height of the square pyramid is **17 units**.