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)

24.1 cm

16.8 m

O91m

14.8 cm

1 answer

First, we can use the formula for the slant height of a square pyramid to find the height of the triangle. The slant height is the hypotenuse of a right triangle, with the base of the triangle being half the length of one side of the square base of the pyramid (20 m / 2 = 10 m) and the height being the height of the pyramid.

Applying the Pythagorean theorem, we have:

(10 m)^2 + h^2 = (13.5 m)^2

Simplifying:

100 m^2 + h^2 = 182.25 m^2

Subtracting 100 m^2 from both sides:

h^2 = 82.25 m^2

Taking the square root of both sides:

h ≈ 9.1 m

Rounding to the nearest tenth, the height of the tent is approximately 9.1 m.