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.
a. 9.1 m
b. 16.8 cm
c. 24.1 cm
d. 14.8 m
To find the height of the tent, we can use the Pythagorean theorem.
Let's call the height of the tent "h". The slant height of the pyramid is the hypotenuse of the right triangle formed by the height and the base. So we have:
h^2 + (20/2)^2 = 13.5^2
Simplifying this equation gives:
h^2 + 100 = 182.25
Subtracting 100 from both sides gives:
h^2 = 82.25
Taking the square root of both sides gives:
h = √82.25
h ≈ 9.1
So the height of the tent is approximately 9.1 meters. Therefore, the answer is:
a. 9.1 m