For the square pyramid, the lateral edge length is 25 inches and the slant height is 24 inches find the height of the pyramid H round your answer to the nearest whole number hint before finding the length of age 1st need to find the length of r
To find the height of the pyramid, we can use the Pythagorean theorem.
Let r be the length of one side of the square base.
Let H be the height of the pyramid.
According to the hint, we first need to find the length of r. Since the lateral edge length is 25 inches and the square base has four equal sides, the length of one side of the square base is 25/4 inches.
Now, let's use the Pythagorean theorem to find the length of H. We have a right triangle with the slant height (24 inches), one-half of the base side (r/2 inches), and the height (H inches).
Using Pythagorean theorem, we have:
(H)^2 = (r/2)^2 + (24)^2
H^2 = (r^2/4) + 576
H^2 = (r^2 + 2304)/4
To further solve for H, we need to find the value of r. We already know that r = 25/4.
Now, substitute the value of r into the equation:
H^2 = ((25/4)^2 + 2304)/4
H^2 = (625/16 + 2304)/4
H^2 = (625 + 2304*16)/16*4
H^2 = (625 + 36864)/64
H^2 = 37489/64
H = sqrt(37489)/sqrt(64)
H ≈ 6.08
Rounding H to the nearest whole number, we get:
H ≈ 6 inches.
Therefore, the height of the pyramid is approximately 6 inches.
To find the height of the square pyramid, we first need to find the length of r (the slant height of one of the triangular faces). We can use the Pythagorean theorem to do this.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have a right triangle with one side of length 25 inches (lateral edge length) and another side of length 24 inches (slant height). Let's call the unknown third side r.
Using the Pythagorean theorem, we have:
r^2 = (lateral edge length)^2 - (slant height)^2
r^2 = 25^2 - 24^2
r^2 = 625 - 576
r^2 = 49
Taking the square root of both sides, we get:
r = √49
r = 7 inches
Now that we know the length of r, we can find the height of the pyramid H. In a square pyramid, the height H is perpendicular to the base, and it connects the apex (top vertex) to the center of the base.
Since the height H, the slant height (24 inches), and r form a right triangle, we can use the Pythagorean theorem again to find H.
H^2 = (slant height)^2 - r^2
H^2 = 24^2 - 7^2
H^2 = 576 - 49
H^2 = 527
Taking the square root of both sides, we get:
H = √527
H ≈ 22.95 inches
Rounding to the nearest whole number, the height of the pyramid H is approximately 23 inches.
To find the height of the square pyramid, we need to find the value of "r" first.
We can start by using the Pythagorean theorem to find the length of the base diagonal "d" of the pyramid:
d^2 = s^2 + s^2
d^2 = 2s^2
Given that the lateral edge length is 25 inches, we can substitute this value into the equation:
d^2 = 2(25^2)
d^2 = 2(625)
d^2 = 1250
d ≈ √1250
d ≈ 35.355 inches
Next, we can use the slant height and the base diagonal to find the radius "r" of the base of the pyramid:
r^2 = (d/2)^2 - h^2
r^2 = (35.355/2)^2 - 24^2
r^2 ≈ 6.895 inches
Finally, we can find the height "H" of the pyramid using the radius "r" and the slant height:
H = √(slant height^2 - r^2)
H = √(24^2 - 6.895^2)
H ≈ √(576 - 47.592025)
H ≈ √528.407975
H ≈ 23 inches (rounded to the nearest whole number)