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?
To find the height of the square pyramid, we need to first find the length of r.
The slant height, s, is the hypotenuse of a right triangle formed by the height (h) and half the length of the base, which is also the radius (r) of the base of the pyramid.
We can use the Pythagorean theorem to find the radius (r):
s^2 = h^2 + (r/2)^2
Plugging in the values:
24^2 = h^2 + (r/2)^2
576 = h^2 + (r^2/4)
Now we can find the length of r:
r^2/4 = 576 - h^2
r^2 = 2304 - 4h^2
Since it is a square pyramid, the base is a square, so the radius (r) is equal to half the length of the base, which can be written as s = 2r:
25 = 2r
r = 25/2 = 12.5
Now we can substitute the value of r back into the equation to solve for h:
12.5^2 = 2304 - 4h^2
156.25 = 2304 - 4h^2
4h^2 = 2304 - 156.25
4h^2 = 2147.75
h^2 = 2147.75 / 4
h^2 = 536.9375
Taking the square root of both sides to solve for h:
h = sqrt(536.9375)
h ≈ 23.2
Rounded to the nearest whole number, the height of the square pyramid is 23 inches.
To find the height of the pyramid, we need to first find the length of the base of the pyramid, which is equal to the length of its lateral edge.
Given that the lateral edge length (e) is 25 inches, we can conclude that the length of the base (r) is also 25 inches.
Now, let's apply the Pythagorean theorem to find the height (h) of the pyramid.
The equation we can set up is:
(r^2) + (h^2) = (s^2)
Substituting the known values:
(25^2) + (h^2) = (24^2)
Simplifying the equation:
625 + (h^2) = 576
Subtracting 576 from both sides:
h^2 = 576 - 625
Simplifying the right side:
h^2 = -49
Since we cannot take the square root of a negative number, we conclude that there is no real solution for h.
To find the height of the square pyramid, we first need to find the length of r (the base radius). We can use the Pythagorean theorem to find r.
The formula for the slant height (s) of a square pyramid is related to the base edge length (e) and the height (h) by the equation:
s^2 = e^2 + h^2
From the given information, we know that e = 25 in. and s = 24 in. We can substitute these values into the equation and solve for h.
24^2 = 25^2 + h^2
576 = 625 + h^2
To isolate h^2, we subtract 625 from both sides:
h^2 = 576 - 625
h^2 = -49
Since we are looking for the height (h), we discard the negative square root value as it would not make sense in this context.
Taking the positive square root of 49, we get:
h = 7
Therefore, the height of the square pyramid is approximately 7 inches.