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
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(1 point)
To find the height of the pyramid, we first need to find the length of the slant height (s). We are given that the lateral edge length (e) is 25 in. Let's use the Pythagorean Theorem to find the length of the slant height:
s^2 = e^2 + r^2
where r is the apothem of the base. Since this is a square pyramid, the apothem (r) is equal to half the length of one lateral edge (e). Therefore, r = e/2 = 25/2 = 12.5 in.
Now we can substitute the values in the Pythagorean Theorem equation:
s^2 = 25^2 + 12.5^2
s^2 = 625 + 156.25
s^2 = 781.25
To find s, we take the square root of both sides:
s = sqrt(781.25)
s ≈ 27.93 in. (rounded to two decimal places)
Now that we have the value of s, we can use it to find the height (h) of the pyramid. The height (h) is the perpendicular distance from the apex to the base. We can use the Pythagorean Theorem again to find h:
h^2 = s^2 - r^2
h^2 = 27.93^2 - 12.5^2
h^2 = 779.8849 - 156.25
h^2 ≈ 623.6349
Taking the square root of both sides, we find:
h ≈ sqrt(623.6349)
h ≈ 24.97 in. (rounded to two decimal places)
Therefore, the height of the pyramid, h, is approximately 25 inches.