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. The height of the square pyramid is?
We can use the Pythagorean theorem to solve for the height of the pyramid.
In a square pyramid, the slant height, s, is the hypotenuse of a right triangle, with the lateral edge length, e, and the height, h, as the other two sides.
Using the Pythagorean theorem, we have:
s^2 = e^2 + h^2
Substituting the given values, we have:
24^2 = 25^2 + h^2
Simplifying,
576 = 625 + h^2
Rearranging,
h^2 = 576 - 625
h^2 = -49
Since we cannot have a negative height, there is no real solution for h in this case.
Therefore, the height of the pyramid cannot be determined with the given information.
To find the height of the square pyramid, you can use the Pythagorean Theorem.
Let's denote the height as 'h', the lateral edge length as 'e', and the slant height as 's'.
According to the Pythagorean Theorem, the relationship between the height, the slant height, and half the lateral edge length of a pyramid is given by:
h^2 = s^2 - (e/2)^2
Plugging in the values we know, we can calculate the height as follows:
h^2 = 24^2 - (25/2)^2
= 576 - (625/4)
= 576 - 390.625
= 185.375
To find the height, we need to find the square root of 185.375:
h = √185.375
≈ 13.61
Rounding this to the nearest whole number, the height of the square pyramid is approximately 14 inches.
To find the height of the square pyramid, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle formed by the height (h), the slant height (s), and half the lateral edge length (e/2).
Using the Pythagorean Theorem, we can write the equation:
(h)^2 = (s)^2 - (e/2)^2
Plugging in the given values:
(h)^2 = (24)^2 - (25/2)^2
Simplifying:
(h)^2 = 576 - (625/4)
(h)^2 = 576 - 156.25
(h)^2 = 419.75
To find the height (h), we need to take the square root of both sides of the equation:
h ≈ √419.75
Calculating the square root:
h ≈ 20.49
Rounding to the nearest whole number:
h ≈ 20
Therefore, the height of the square pyramid is approximately 20 inches.