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 r . (1 point) The height of the square pyramid is in. Skip to navigation
To find the height of the pyramid, we first need to find the length of the slant height, r.
Using the Pythagorean theorem, we can find r:
r^2 = e^2 - (s/2)^2
r^2 = 25^2 - (24/2)^2
r^2 = 625 - 12^2
r^2 = 625 - 144
r^2 = 481
r ≈ √481
r ≈ 21.93 in (rounded to two decimal places)
Now, we can find the height, h, using the Pythagorean theorem:
h^2 = s^2 - r^2
h^2 = 24^2 - 21.93^2
h^2 = 576 - 481
h^2 = 95
h ≈ √95
h ≈ 9.75 in (rounded to two decimal places)
Therefore, the height of the pyramid is approximately 10 inches.