Question

A circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent. Round the answer to the nearest tenth. (1 point) 16.8 m 14.8 cm 91m 24.1 cm

Answer 1

To find the height of the circus tent in the shape of a square pyramid, we can use the given dimensions—specifically, the edge of the square base and the slant height.

1. **Identify the dimensions**:
- Each edge of the square base \( s = 20 \, \text{m} \).
- Slant height \( l = 13.5 \, \text{m} \).

2. **Find the half of the base edge**:
- The distance from the center of the base to a vertex (the base radius) is half the length of the edge:
\[
r = \frac{s}{2} = \frac{20}{2} = 10 \, \text{m}.
\]

3. **Use the Pythagorean theorem** to find the height \( h \) of the pyramid. The relationship between the height \( h \), the slant height \( l \), and the radius \( r \) can be expressed as:
\[
l^2 = h^2 + r^2.
\]

4. **Substitute the known values into the equation**:
\[
(13.5)^2 = h^2 + (10)^2.
\]
\[
182.25 = h^2 + 100.
\]

5. **Solve for \( h^2 \)**:
\[
h^2 = 182.25 - 100,
\]
\[
h^2 = 82.25.
\]

6. **Take the square root to solve for \( h \)**:
\[
h = \sqrt{82.25} \approx 9.1 \, \text{m}.
\]

Since none of the given options correctly represent \( 9.1 \, \text{m} \), we should check the values available:
- 16.8 m
- 14.8 cm
- 91 m
- 24.1 cm

Given that we calculated around \( 9.1 \, \text{m} \), the previously provided options do not match the calculations.

It seems there is a misunderstanding in the options given.

Does the tent have a different height indicated by different slant height or base length? Or could there be an error in the question options?

My calculated height is \( 9.1 \, \text{m} \). If the options are meant to be more than the calculated value, it indicates either a required different context for the problem or an alternative finding should be assumed.