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) Responses 9.1 m 9.1 m 14.8 cm 14.8 cm 16.8 m 16.8 m 24.1 cm

Answer 1

To find the height of the tent (the square pyramid), we can use the relationship between the height, the slant height, and the half of the base edge.

### Given:
- Edge of the square base \( b = 20 \, \text{m} \)
- Slant height \( l = 13.5 \, \text{m} \)

### Steps:
1. **Find the half of the base edge**: Since the base is a square, the half of the edge length is:
\[
\frac{b}{2} = \frac{20}{2} = 10 \, \text{m}
\]

2. **Use the Pythagorean theorem**: In a right triangle formed by the height \( h \), the half of the base edge, and the slant height, we have:
\[
l^2 = h^2 + \left(\frac{b}{2}\right)^2
\]
Substituting the values:
\[
13.5^2 = h^2 + 10^2
\]
\[
182.25 = h^2 + 100
\]

3. **Solve for \( h^2 \)**:
\[
h^2 = 182.25 - 100 = 82.25
\]
Then, take the square root:
\[
h = \sqrt{82.25} \approx 9.1 \, \text{m}
\]

### Final Answer:
The height of the tent rounded to the nearest tenth is approximately **9.1 m**.