Question
What is the slant height of the pyramid?
14 m
Slant Height
28 m
(This figure is not drawn to scale.)
Question content area bottom
Part 1
The slant height is about
enter your response here m.
(Round to the nearest tenth as needed.)
14 m
Slant Height
28 m
(This figure is not drawn to scale.)
Question content area bottom
Part 1
The slant height is about
enter your response here m.
(Round to the nearest tenth as needed.)
Answers
GPT-4o mini
To determine the slant height of the pyramid, we typically need to know the dimensions of the base and the height of the pyramid. However, based on the numbers you've provided (14 m and 28 m), it seems that there might be some confusion about the specific measurements required.
If you meant that the base edge of the pyramid is 14 m and the total height of the pyramid is 28 m (or vice versa), we can use the Pythagorean theorem to find the slant height.
Assuming the slant height (l) corresponds to the height from the middle of one edge of the base (which we can consider as half the base edge) to the apex, we can use the following equation:
\[
l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2}
\]
Where:
- \(h\) is the vertical height of the pyramid,
- \(b\) is the base edge.
Let's apply the Pythagorean theorem assuming:
- \(h = 28\) m (the vertical height)
- \(b = 14\) m (the base edge)
First, calculate \(\frac{b}{2}\):
\[
\frac{b}{2} = \frac{14}{2} = 7 \text{ m}
\]
Now plug these values into the Pythagorean theorem formula:
\[
l = \sqrt{28^2 + 7^2} = \sqrt{784 + 49} = \sqrt{833}
\]
Calculating \(\sqrt{833}\):
\[
l \approx 28.8 \text{ m}
\]
When rounded to the nearest tenth, the slant height is approximately \(28.8\) m.
Please confirm if the base edge and height values are indeed what you described, or let me know if there are additional details!
If you meant that the base edge of the pyramid is 14 m and the total height of the pyramid is 28 m (or vice versa), we can use the Pythagorean theorem to find the slant height.
Assuming the slant height (l) corresponds to the height from the middle of one edge of the base (which we can consider as half the base edge) to the apex, we can use the following equation:
\[
l = \sqrt{h^2 + \left(\frac{b}{2}\right)^2}
\]
Where:
- \(h\) is the vertical height of the pyramid,
- \(b\) is the base edge.
Let's apply the Pythagorean theorem assuming:
- \(h = 28\) m (the vertical height)
- \(b = 14\) m (the base edge)
First, calculate \(\frac{b}{2}\):
\[
\frac{b}{2} = \frac{14}{2} = 7 \text{ m}
\]
Now plug these values into the Pythagorean theorem formula:
\[
l = \sqrt{28^2 + 7^2} = \sqrt{784 + 49} = \sqrt{833}
\]
Calculating \(\sqrt{833}\):
\[
l \approx 28.8 \text{ m}
\]
When rounded to the nearest tenth, the slant height is approximately \(28.8\) m.
Please confirm if the base edge and height values are indeed what you described, or let me know if there are additional details!