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

16.8 m 

9.1 m 

24.1 cm

14.8 cm

Answer 1

To find the height of the square pyramid (circus tent), we can use the Pythagorean theorem. The height \( h \), the slant height \( l \), and the distance from the center of the base to the midpoint of one edge (half the length of the base) form a right triangle.

1. **Calculate the half of the base edge**:
\[
\text{Half of base edge} = \frac{20 \text{ m}}{2} = 10 \text{ m}
\]

2. **Use the Pythagorean theorem**:
\[
l^2 = h^2 + \left(\frac{\text{base edge}}{2}\right)^2
\]
Where:
- \( l = 13.5 \) m (slant height)
- Base edge = 20 m

3. **Substituting the values**:
\[
13.5^2 = h^2 + 10^2
\]
\[
182.25 = h^2 + 100
\]

4. **Rearranging the equation to solve for \( h^2 \)**:
\[
h^2 = 182.25 - 100
\]
\[
h^2 = 82.25
\]

5. **Taking the square root of both sides to find \( h \)**:
\[
h = \sqrt{82.25} \approx 9.1 \text{ m}
\]

Thus, the height of the tent rounded to the nearest tenth is:

**9.1 m**.