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?
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, the slant height (s) is the hypotenuse and the lateral edge length (e) and the height (h) are the other two sides of the right triangle.
Using the Pythagorean theorem equation:
s^2 = e^2 + h^2
Plugging in the given values:
24^2 = 25^2 + h^2
576 = 625 + h^2
Rearranging the equation:
h^2 = 576 - 625
h^2 = -49
Since the square of a real number cannot be negative, there is no valid solution for the height of the square pyramid using the given values of the slant height and lateral edge length.
Therefore, the height of the pyramid cannot be determined.
We can use the Pythagorean theorem to solve for the height of the square pyramid.
The lateral edge length, e, represents the length of the base of the square pyramid. Since it is a square, all sides are equal and each side length is also 25 in.
Let's call the height of the pyramid h. One face of the pyramid is a right triangle with legs of length h and e/2 (half the length of the base). The slant height, s, is the hypotenuse of this right triangle.
So we can use the Pythagorean theorem: h^2 + (e/2)^2 = s^2
Plugging in the given values, we get: h^2 + (25/2)^2 = 24^2
Simplifying: h^2 + 625/4 = 576
Multiplying both sides by 4 to get rid of the fraction: 4h^2 + 625 = 2304
Subtracting 625 from both sides: 4h^2 = 1679
Dividing both sides by 4: h^2 = 1679/4
Taking the square root of both sides: h = sqrt(1679/4)
Rounding to the nearest whole number: h ≈ 32
So the height of the square pyramid is approximately 32 inches.
To find the height of the square pyramid, you can use the Pythagorean theorem. The lateral edge length (e) and the slant height (s) are given. Let's label the height as 'h'.
The slant height (s) is the hypotenuse of the right triangle formed by the height (h) and half the base of the square at the bottom of the pyramid.
Using the Pythagorean theorem, we have:
s^2 = h^2 + (0.5b)^2,
where b is the length of the base of the square pyramid.
In the case of a square pyramid, the base is a square with sides equal to e.
Now, substituting the given values:
24^2 = h^2 + (0.5e)^2,
576 = h^2 + (0.5 * 25)^2,
576 = h^2 + (0.5)^2(25)^2,
576 = h^2 + 0.25(625),
576 = h^2 + 156.25.
To isolate h^2, subtract 156.25 from both sides:
h^2 = 576 - 156.25,
h^2 = 419.75.
Now, take the square root of both sides to find h:
h = √(419.75),
h ≈ 20.49.
Round the answer to the nearest whole number:
The height of the square pyramid is approximately 20 inches.