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)

To find the height of the square pyramid (the tent) with a square base and a given slant height, we can use the Pythagorean theorem.

1. Identify the dimensions:

   • The length of each edge of the square base (\(b\)) = 20 m.
   • The slant height (\(l\)) = 13.5 m.

2. Find the length of the diagonal from the center of the base to a vertex:

   • The distance from the center of the base to the midpoint of one of the edges is \( \frac{b}{2} = \frac{20 , \text{m}}{2} = 10 , \text{m} \).
   • The full diagonal from the center of the base to a vertex can be calculated using the Pythagorean theorem: \[ \text{distance from center to vertex} = \sqrt{\left(\frac{b}{2}\right)^2 + \left(\frac{b}{2}\right)^2} = \sqrt{10^2 + 10^2} = \sqrt{200} = 10\sqrt{2} , \text{m} \approx 14.14 , \text{m} \]

3. Apply the Pythagorean theorem to find the height (\(h\)):

   • In the right triangle formed by the height \(h\), the slant height \(l\), and the distance from the center to a vertex, we have the equation: \[ l^2 = h^2 + \left(\frac{b}{2}\right)^2 \]
   • Plugging in the values we know: \[ (13.5)^2 = h^2 + (10)^2 \] \[ 182.25 = h^2 + 100 \] \[ h^2 = 182.25 - 100 \] \[ h^2 = 82.25 \] \[ h = \sqrt{82.25} \approx 9.1 , \text{m} \]

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