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 14.8 cm 14.8 cm 9.1 m 9.1 m 24.1 cm 24.1 cm 16.8 m

Answer 1

To find the height of the square pyramid (circus tent), we can use the Pythagorean theorem.

1. First, calculate the half-length of the base, which is:
\[
\frac{20 \text{ m}}{2} = 10 \text{ m}
\]

2. We know the slant height of the pyramid (the distance from the apex of the pyramid to the midpoint of a side of the base) is 13.5 m.

3. Let's denote the height of the pyramid as \( h \). Now we have a right triangle where:
- One leg is the height \( h \),
- The other leg is the half-length of the base (10 m),
- The hypotenuse is the slant height (13.5 m).

According to the Pythagorean theorem:
\[
h^2 + (10 \text{ m})^2 = (13.5 \text{ m})^2
\]

4. Substituting the values:
\[
h^2 + 100 = 182.25
\]

5. Rearranging to solve for \( h^2 \):
\[
h^2 = 182.25 - 100 = 82.25
\]

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

Therefore, the height of the tent rounded to the nearest tenth is **9.1 m**.