Use the image to answer the question. 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 rr . (1 point)
To find the height of the pyramid, we first need to find the length of the perpendicular height, which we will call "r".
Using the Pythagorean Theorem, we can find the length of "r":
r^2 + e^2 = s^2
r^2 + 25^2 = 24^2
r^2 + 625 = 576
r^2 = 576 - 625
r^2 = 49
r = √49
r = 7
Now that we have found the length of "r", we can find the height of the pyramid, which is the perpendicular height from the apex to the base. The height of the pyramid, "h", can be found by using the Pythagorean Theorem with the base edge length, which is 25 in., and the perpendicular height, which is 7 in.
h^2 + 12.5^2 = 25^2
h^2 + 156.25 = 625
h^2 = 625 - 156.25
h^2 = 468.75
h = √468.75
h ≈ 21
The height of the pyramid is approximately 21 inches.