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
14.8 cm
14.8 cm
16.8 m
To find the height of the tent, we can use the Pythagorean theorem. The height is the hypotenuse of a right triangle with one leg being the height of the pyramid (h) and the other leg being half the length of the base (10 m).
Using the Pythagorean theorem, we have:
h^2 = (10 m)^2 + (13.5 m)^2
h^2 = 100 m^2 + 182.25 m^2
h^2 = 282.25 m^2
Taking the square root of both sides, we find:
h ≈ √282.25 m^2
h ≈ 16.8 m
Therefore, the height of the tent is approximately 16.8 m.