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

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.