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
16.8 m
16.8 m
9.1 m
9.1 m
To find the height of the tent, we can use the Pythagorean Theorem. The height, slant height, and half the length of the base form a right triangle.
Let's label the height as "h", the slant height as "s", and half the length of the base as "b/2".
Using the Pythagorean Theorem, we have:
h^2 + (b/2)^2 = s^2
h^2 + (10)^2 = (13.5)^2
h^2 + 100 = 182.25
h^2 = 182.25 - 100
h^2 = 82.25
Taking the square root of both sides, we get:
h = √82.25
h ≈ 9.1
Therefore, the height of the tent is approximately 9.1 m.