Question

The circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and it's slant height is 13.5 m. Find the height of the tent. Round to the nearest tenth

Answer 1

To find the height of a square pyramid (the circus tent in this case) with a square base and known slant height, we can use the Pythagorean theorem.

1. **Identify the elements**:
- The length of each edge of the square base \( a = 20 \) m.
- The slant height \( l = 13.5 \) m.

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

3. **Use the Pythagorean theorem**:
The slant height \( l \), the height \( h \) of the pyramid, and half of the base edge form a right triangle. Using the Pythagorean theorem:
\[
l^2 = h^2 + \left(\frac{a}{2}\right)^2
\]

Substituting the known values:
\[
(13.5)^2 = h^2 + (10)^2
\]

This simplifies to:
\[
182.25 = h^2 + 100
\]

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

5. **Find \( h \)**:
\[
h = \sqrt{82.25} \approx 9.1 \text{ m}
\]

Therefore, the height of the tent, rounded to the nearest tenth, is approximately \( \boxed{9.1} \) meters.