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

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

1 answer

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

  1. The base of the pyramid is a square with each edge measuring 20 m, so the length of half of one edge (the base's half-diagonal) is: \[ \frac{20}{2} = 10 , \text{m} \]

  2. The slant height of the pyramid is given as 13.5 m. The height (h) of the pyramid, the slant height (l), and half of the base edge (10 m) forms a right triangle. According to the Pythagorean theorem: \[ l^2 = h^2 + (10)^2 \] Plugging in the values, we have: \[ (13.5)^2 = h^2 + 10^2 \] \[ 182.25 = h^2 + 100 \]

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

  4. Taking the square root of both sides to find \(h\): \[ h = \sqrt{82.25} \approx 9.1 , \text{m} \]

Therefore, the height of the tent is approximately \(9.1 , \text{m}\).

The final answer is: 9.1 m