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
9.1 m
9.1 m
24.1 cm
24.1 cm
16.8 m
16.8 m
14.8 cm
To find the height of the tent, we can use the Pythagorean Theorem.
The slant height of the pyramid is the hypotenuse of a right triangle formed by one edge of the base and the height of the pyramid.
Let h be the height of the pyramid.
Using the Pythagorean Theorem, we have:
h^2 + (10m)^2 = (13.5m)^2
h^2 + 100m^2 = 182.25m^2
h^2 = 182.25m^2 - 100m^2
h^2 = 82.25m^2
h = √(82.25m^2)
h ≈ 9.1 m
Therefore, the height of the tent is approximately 9.1 m.
Answer: 9.1 m