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)
• 14.8 ст
• 24.1 ст
• 9.1 m
• 16.8 m
To find the height of the tent, we can use the Pythagorean theorem.
The slant height of the tent forms the hypotenuse of a right triangle, with the height of the tent as one of the legs, and half the length of the base of the tent (10 m) as the other leg.
Let the height of the tent be h.
Using the Pythagorean theorem, we have:
h^2 + 10^2 = 13.5^2
h^2 + 100 = 182.25
h^2 = 82.25
h ≈ √82.25 ≈ 9.1 m
Therefore, the height of the tent is approximately 9.1 m.
The correct answer is: • 9.1 m
To find the height of the tent, we can use the formula for the slant height of a square pyramid:
slant height = √(base length/2)^2 + height^2
In this case, the base length is 20 meters, and the slant height is given as 13.5 meters. Let's substitute these values into the formula and solve for the height:
13.5 = √(20/2)^2 + height^2
13.5 = √(10)^2 + height^2
13.5 = √100 + height^2
13.5 = 10 + height^2
13.5 - 10 = height^2
3.5 = height^2
To find the height, we need to take the square root of both sides of the equation:
√(3.5) = √(height^2)
1.87 ≈ height
Therefore, the height of the tent is approximately 1.87 meters. Rounding to the nearest tenth, we get:
height ≈ 1.9 m
So, the correct answer is not provided among the options.
To find the height of the tent, we can use the Pythagorean Theorem.
In a square pyramid, the slant height is the hypotenuse of a right triangle formed by one edge of the base, the height, and the slant height.
Let h be the height of the tent.
By the Pythagorean Theorem, we have:
h^2 + 10^2 = 13.5^2
Simplifying this equation, we get:
h^2 + 100 = 182.25
Subtracting 100 from both sides, we have:
h^2 = 82.25
Taking the square root of both sides, we get:
h = √82.25
Rounding to the nearest tenth, the height of the tent is approximately 9.1m.
Therefore, the answer is:
• 9.1 m