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
.
(1 point)
The height of the square pyramid is
in.
To find the height of the square pyramid, we need to find the length of the slant height (s) and the lateral edge length (e). We are also given that the slant height is 24 in and the lateral edge length is 25 in.
To find the length of the height (h), we first need to find the length of the base radius (r).
The base of the square pyramid is a square, so all sides are equal. The base is formed by four lateral edges, and each lateral edge connects two adjacent vertices of the square base. The lateral edges meet at the apex (top) of the pyramid.
In a square pyramid, the slant height (s) is the distance from the apex to the midpoint of one side of the base. So, s is equal to the length of one lateral edge.
We are given that the lateral edge length (e) is 25 in, so we know that e = s.
Now that we know e = s = 25 in, we can find the length of the base radius (r) using the formula:
r = e / (2 * pi)
Plugging in the value of e, we get:
r = 25 / (2 * pi) ≈ 3.98 in (rounding to two decimal places)
Now that we know the radius (r), we can find the height (h) using the Pythagorean theorem:
h^2 = s^2 - r^2
Plugging in the values of s and r, we get:
h^2 = 24^2 - 3.98^2
h^2 ≈ 552.04
h ≈ square root of 552.04 ≈ 23.5 in (rounding to the nearest whole number)
Therefore, the height of the square pyramid is approximately 23 inches.
To find the height of the pyramid, we first need to find the length of the diagonal of the square base (which is also the length of r).
Let's use the Pythagorean theorem to find the length of r.
The lateral edge length of the pyramid, e, is given as 25 inches. Since the base of a square pyramid is a square, the length of each side of the square base is also 25 inches.
Let's draw a right triangle with one leg as the height (h), the other leg as half the length of the base (25/2 = 12.5), and the hypotenuse as the slant height (s = 24).
Using the Pythagorean theorem:
r^2 = (12.5)^2 + (24)^2
r^2 = 156.25 + 576
r^2 = 732.25
r ≈ 27.04 inches (rounded to two decimal places)
Now that we have the length of r, we can find the height (h) of the pyramid.
Using the Pythagorean theorem again:
h^2 = s^2 - r^2
h^2 = 24^2 - 27.04^2
h^2 = 576 - 732.25
h^2 ≈ -156.25
However, the square of a real number cannot be negative. This implies that there is no real solution for h.
So, the height of the square pyramid cannot be determined with the given information.
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
.
(1 point)
Apologies for the previous incorrect response.
To find the height of the pyramid, we can use the Pythagorean theorem.
The lateral edge length, e, is the length of the diagonal of each face of the square base. In a square pyramid, the diagonal is equal to the square root of 2 times the length of one of the sides of the square base.
Given that e = 25 inches, we can find the length of each side of the square base as follows:
s = √2 * side_length
25 = √2 * side_length
side_length = 25 / √2 ≈ 17.68 inches
Now that we have the length of one side of the square base, let's find the length of the diagonal of the square base (r). The diagonal of a square is found using the Pythagorean theorem:
r^2 = side_length^2 + side_length^2
r^2 = 17.68^2 + 17.68^2
r^2 = 622.7424 + 622.7424
r^2 ≈ 1245.48
r ≈ √1245.48 ≈ 35.29 inches (rounded to two decimal places)
Finally, to find the height (h) of the pyramid, we can use the Pythagorean theorem again:
h^2 = s^2 - r^2
h^2 = 24^2 - 35.29^2
h^2 = 576 - 1245.48
h^2 ≈ -669.48
Again, we have a negative value, meaning there is no real solution for h.
Therefore, the height of the square pyramid cannot be determined with the given information.