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
24.1 cm
24.1 cm
9.1 m
9.1 m
16.8 m
To find the height of the tent, we can use the Pythagorean theorem.
Let's label the height of the pyramid as 'h' and the length of the slant height as 's'. We know that the length of one edge of the square base is 20 m.
Using the Pythagorean theorem, we have the following equation:
h^2 + (20/2)^2 = 13.5^2
Simplifying this equation, we have:
h^2 + 10^2 = 13.5^2
h^2 + 100 = 182.25
h^2 = 82.25
Taking the square root of both sides, we find:
h ≈ 9.1 m
Therefore, the height of the tent is approximately 9.1 m.