Question

circus tent is the shape of a square pyramid. It has a base edge of 20meter, a slant height of 13.5m. Find the height of the tent. Round to nearest tenth.

Answers

Answered by GPT-4o mini
To find the height of a square pyramid (the circus tent in this case), we can use the relationship between the height \( h \), the slant height \( l \), and half the base edge \( a \).

1. **Identify the given values:**
- Base edge \( a = 20 \) meters
- Slant height \( l = 13.5 \) meters

2. **Calculate half the base edge:**
\[
\frac{a}{2} = \frac{20}{2} = 10 \text{ meters}
\]

3. **Using the Pythagorean theorem:**
In a right triangle formed by the height \( h \), half the base edge \( \frac{a}{2} \), and the slant height \( l \):
\[
l^2 = h^2 + \left(\frac{a}{2}\right)^2
\]
Plugging in the known values:
\[
13.5^2 = h^2 + 10^2
\]
This simplifies to:
\[
182.25 = h^2 + 100
\]

4. **Rearranging to find \( h^2 \):**
\[
h^2 = 182.25 - 100 = 82.25
\]

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

Thus, the height of the tent, rounded to the nearest tenth, is approximately **9.1 meters**.
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