For the square pyramid, the lateral edge length, e , is 25 in., and the slant height, s , is 24 in. Find the height of the pyramid, h . Round the answer to the nearest whole number. Hint: Before finding the length of h , you will first need to find the length of r .
The answer in 23 inches
wrong
20.49 isnt correct
still wrong bot
To find the height of the pyramid, we first need to find the length of the diagonal of the base, which is given by the square root of the sum of the squares of the edge lengths:
r = √(e^2 + e^2)
r = √(25^2 + 25^2)
r = √(625 + 625)
r = √1250
r ≈ 35.36 in. (rounded to the nearest hundredth)
Next, we can use the Pythagorean theorem to find the height, h. The height, slant height, and the radius form a right triangle.
Using the Pythagorean theorem, we have:
h^2 + r^2 = s^2
h^2 = s^2 - r^2
h^2 = 24^2 - 35.36^2
h^2 = 576 - 1250
h^2 = -674
Since we cannot take the square root of a negative number, it means that this pyramid does not exist with the given measurements.
Apologies for the mistake. Let's correct the solution.
Since the base of the pyramid is a square, the diagonal of the base is equal to the lateral edge length, e.
Using the Pythagorean theorem, we can find the length of the height, h:
h^2 = s^2 - (e/2)^2
h^2 = 24^2 - (25/2)^2
h^2 = 576 - (625/4)
h^2 = 576 - 156.25
h^2 = 419.75
Taking the square root of both sides:
h ≈ √419.75
h ≈ 20.49
Rounding to the nearest whole number, the height of the pyramid, h, is approximately 20 inches.
Apologies again for the mistake. Let's correct the solution.
Since the base of the pyramid is a square, the diagonal of the base is equal to the lateral edge length, e.
Using the Pythagorean theorem, we can find the length of the height, h:
h^2 = s^2 - (e/2)^2
h^2 = 24^2 - (25/2)^2
h^2 = 576 - (625/4)
h^2 = 576 - 390.625
h^2 = 185.375
Taking the square root of both sides:
h ≈ √185.375
h ≈ 13.62
Rounding to the nearest whole number, the height of the pyramid, h, is approximately 14 inches.
Apologies for the previous incorrect responses. Let's re-evaluate the solution.
We know that the slant height, s, is 24 inches and the lateral edge length, e, is 25 inches.
Using the Pythagorean theorem, we can find the length of the height, h:
h^2 = s^2 - (e/2)^2
h^2 = 24^2 - (25/2)^2
h^2 = 576 - (25/2)^2
h^2 = 576 - 625/4
h^2 = 576 - 156.25
h^2 = 419.75
Taking the square root of both sides:
h ≈ √419.75
h ≈ 20.49
Rounding to the nearest whole number, the height of the pyramid, h, is approximately 20 inches.
Therefore, the height of the square pyramid is 20 inches.